I want to do my best to give you as much information as possible to help you with your queries.
Assuming you are a US citizen all you need to visit Japan for 90 days is a valid US Passport. I do know someone who arrived in Japan with an expired Passport. Don't be that person.
When flying Internationally, I don't tend to check-in on line, because I almost always want to check a bag since it's free and it's just easier to do that at the airport. If your JAL flight did not include a seat assignment you can book one 24 hours in advance of your departure when you check in on-line. After checking in, you can either have an e-ticket sent to your cell phone or print out a ticket or just re-check-in with the staff when you take up your suitcase and they will give you a boarding pass. For International flights I do tend to use the staff at the airport check-in to receive ticketing, and they will give me my boarding pass. All I need is my passport for them to find me in the system, if that were to ever fail I would use the email confirmation.
The best way to figure out exactly where your hotel is, is Google Maps. Many people rent SIM Cards or rent a cell phone or rent pocket WiFi while in Japan. I happen to be on Project Fi, Google's cell phone service, and when I turn on roaming my cell phone works in Japan as is. I will occasionally have dropped texts to Japanese numbers, but the internet and calls always work and I can text people in the USA just fine. It's cheaper than renting a SIM or pocket WiFi for me.
You can use Google Maps now to get some idea where your hotels are. So for example, your hotel in Tokyo while in Shinjuku is actually much closer to Shin-Okubo and Okubo train stations. Both are on JR lines (the Yamanote and Sobu respectively.) Your hotel in Osaka is near Nishitanabe subway station. The subway is NOT covered by a JR pass. Most JR (Japan Railways) passes only cover trains owned by JR. They don't cover the subway.
I am still a huge fan of hyperdia http://www.hyperdia.com/
for finding how often trains or subways run. I've not used them for bus routes, but I tend to prefer trains and subways.
Yes, when you get a train you must wait for your stop. Depending on the train and your stop it could be a long wait or a short wait. The shinkansen or bullet trains make the announcements in English and in Japanese for all stops. They play a helpful chime to let you know you are approaching the station so you can gather your belongings. Other trains and the subway frequently have a screen inside the car letting you know what the next station is in both Japanese and English characters. All train and subway stations I've ever seen are also always written out in Japanese and English characters. You really just need to stop and take a deep breath and look around.
For taking JR trains with a pass, just look for the manned ticket windows and show your JR pass. If you want to reserve seats for a train, you would go to a manned ticket office in a larger station and let them know where you would like to go and approximately what time.
However, I am not sure a JR Pass actually works for you. A 14 day Pass will not pay off with the travel you currently have listed. A 7 day Pass also won't work since you say you are in Osaka Sunday to Sunday. To get a 7 day to barely work, you would need to leave on a Sunday and return to Tokyo on Saturday the last day of your pass. (Sun (day 1); Mon (day 2); Tues (day 3), Wed (day 4); Thurs (day 5); Fri (day 6); and Sat (day 7.) A JR pass will not cover any of the subway transport you plan to use in Osaka.
You might be better off getting a JR East discounted Narita express ticket for helping you take the Narita Express from Narita to Tokyo roundtrip. https://www.jreast.co.jp/e/pass/nex_round.html
For travel around Tokyo/Osaka you will want to get some sort of IC card. Since you're starting in Tokyo it would make sense to get a Pasmo or Suica. Other than the picture and where it is purchased, there will not be a lot of differences for your purposes between the two. A Suica can be bought at any large JR Station. It's an IC card that you put money on (like 1000 yen) and then you just tap it to go through the gates to take a train or subway. IC cards can also be used on many buses. I have a Suica Card as does my daughter. A Pasmo is the same sort of IC card, it was just bought at a subway station vs. a JR Station. It will still work for JR trains as long as there is money on it. You can read about them here: https://www.japan-guide.com/e/e2359_003.html
There are pictures showing the car readers. You need to put down a refundable 500 yen deposit to have an IC card. an IC card would be valid for the subways in Osaka, and you will need to take the subway to get to most tourist places in Osaka from your hotel.
So in the case you decide to buy the discounted JR NEX ticket I linked to above you would do the following: After going through Customs head to ground transport which is one or two levels lower. There will be a JR East office with signs in English lettering. Go there and buy your special discounted JR Nex ticket. If you have a pass, you can also turn it in there so you have your official actual pass vs. the pass order which is what you received in the mail. They will help you book a NEX to Shinjuku. You will take your tickets and either go through the gates or if you are feeling unsure there is a manned entrance and you can go through there. You will then take another escalator to the actual track. You will then look at your ticket which will tell you an exact time for your train, a track number, a car number and a seat number. There will be signs for car numbers and go to the one on your ticket. If you are confused ask someone for help. There will be a chime a few moments before your train arrives. Enter the train and find your assigned seat. Make sure the train is the train you have a ticket for and not a train going elsewhere. Your NEX will not stop again (since I believe JAL is in terminal 1 if your flight for some reason came into terminal 2, the train will start at your station and you can watch the people clean it before they allow boarding. In that case, the 1st stop will be Terminal 1.) until you reach Tokyo Station. A chime will play a few minutes before and a voice will let you know in English that you are arriving at Tokyo Station. Do not exit. You will stay at Tokyo Station a bit longer because the trains tend to split there and one part goes down to Yokohama and the other half goes to Shinjuku, which is why it's important you told the staff at the JR Office you wanted Okubo or Shin-Okubo. They will know you want a ticket to Shinjuku then. I believe the train will then often stop in Shibuya and then in Shinjuku. Once on the platform you will have some walking to do to transfer to another line to get closer to your hotel. If you were to exit Shinjuku Station here, you would have a little more than 2 kms to walk to get to your hotel. It can be walked, but depending on how much luggage you have and the time of day the streets could be crowded. So assuming you stay in Shinjuku Station, you will walk along the platform towards the signs that say transfer to either the Sobu line (pale yellow) or Yamanote line (lime green) Once you find the tracks for the Sobu or Yamanote, you need to get on in the right direction. In the case of the Sobu, you are heading towards Nakano or Mitaka. In the case of the Yamanote, it's Ikebukuro. Either line you would take one station. On the Sobu, it's one station to Okubo Station and on the Yamanote line it is one station to Shin-Okubo. At Okubo you will look for signs in English for the South exit. You can go through a manned gate, since it is easier if you've never done this before. The Shin-Okubo exit on the Yamanote line will be a slightly longer walk since there only is one exit. Based on the pictures I am seeing on Google Maps Shin-Okubo only has stairs, while the North exit of Okubo exit has an elevator. Depending on the amount of luggage you have you might prefer the elevator to taking the closer but stairs only South exit. From there you would walk to your hotel, it should be no more than 5 minutes. I've never stayed in that area and I've not been to that area in about decade. There use to be a lovely vegan lunch place in that area and I went there a few times.
I hope this helps!