I'm back, watching World cup games will not let me sleep :)
Back to Q, but first, I recommend use this Pass before answering the new Qs.
It should be easier to understand by looking at the route map.http://www.sendaiareapass.jp/en/index.html
A) Sendai sta./仙台駅前(-eki mae) to Jogi/定義https://www.navitime.co.jp/bus/busrailroadlist/?id=00081728
Bus route No.S844, S845 and 846.
Click 時刻表(jikoku-hyo = timetable) and 路線図(rosen-zu = route map).
Click each dep time will be showing all stopping bus stops, also you can enlarge route map.
There are three different bus route numbers, this reason is very simple,
they runs three different routes only near last stop Jogi, Okura dam lake side.https://www.pref.miyagi.jp/uploaded/image/36820.jpg
Last stop Jogi area will be upstream of this dam lake.
Some buses doesn't operate on weekdays(平日 hei-jitsu),
Sat(土曜日 doyo-bi), or Sun and National holidays(休日kyu-jitsu), check them all.
It is the same as the current timetable even at that time.
Also you can search train(JR Senzan line) timetable at Google Maps without Japanese,
input "Sendai to Ayashi" and then change dep date and time enough like this.https://goo.gl/maps/y1VZowBqZjt
And no plan to revise all timetables, including below.
B)Jogi to Ayashi eki-mae(愛子駅前), NOT "Ayashi-eki" bus stop.https://www.navitime.co.jp/poi?node=00144669
Bus route No.S844 and S845, both all buses will be stopping no worry.
Both bus destination is "for Sendai sta.", on the way of same route.
Around 35 min ride, if no big traffic jam.
The in-car broadcast of the bus is automatic voice and no English.
If you tell the driver in advance until dep, driver will tell it by own mic.
Do not forget to press the get off button,
in Japanese, "Tsugi-wa(次は、つぎは)" means "Next (stop) is".http://www.kotsu.city.sendai.jp/english/bus/norikata.html
(Discounted Pass will only show it to the driver at getting off, no need to take a boarding ticket.)
On train, there is automatic English broadcast after Japanese and no stop button, though.
C)Ayashi-eki(愛子駅) to AkiuOtaki(秋保大滝)https://www.navitime.co.jp/bus/diagram/direction/00144505
Only bus route No.87, bus destination is "for Futakuchi(二口)".
Checking it now, on weekdays and Saturdays only at 13 o'clock
and holiday at 11 o'clock, so planning is impossible on holidays.
D)AkiuOtaki to Sendai sta.
This route has only a problem. (not so serious)
BC no good time dep bus that back to Ayashi sta.,
will be only staying for 1 hour is too short, means no enough time to explorer around.
But, other company's direct bus(Pass covered) is operated and dep 2 hour latar until Sendai sta.
However, no operating on weekday, this is no good and may a big problem.https://www.navitime.co.jp/diagram/bus/00144635/00072443/0/
You can also call a taxi, but on weekday if I were you, will try hitchhike
until AkiuOnsen(hot springs town), or AkiuBunka-no-sato Center(秋保文化の里センター)
where the number of buses up to "Senadai sta." will increase, not so far.https://goo.gl/maps/U1rySRMuEPnhttps://goo.gl/maps/rGnNRpGi53nhttps://www.navitime.co.jp/diagram/bus/00144621/00072443/0/
If on Sat weather will be fine blue sky, you should go, watch weather forecast.
And after AkiuOnsen taking this bus, but operating route is quite different,
bus will be stopping via "Nagamachi sta.(長町駅)" route, means time longer.
So getting off at Nagamachi-minami sta.(長町南駅) bus stop,https://goo.gl/maps/sRcGSXjcMRy
(time is not a bus)
then switch to a City Subway via Sendai sta. train is the best. (all trains will be stopping)https://goo.gl/maps/kWm52UVPjPH2
In case of train, Pass just incert automatic ticket gate enough.("JR" line,too)http://www.kotsu.city.sendai.jp/english/subway/norikata.htmlhttps://youtu.be/hScqnnrFpw0
For these all buses, JR trains and City Subway trains, Pass covered.
Just going from Sendai sta. to Jogi without discount cost is about 1100Y,
so you can get around 60% of benefits as total.
And basically this pass is only for foreign tourists for "one day",
but there is mostly same pass sales for "two days" that anyone can buy.
So this pass may be better if stay for more than two days.
The place of sale is the same and pass name changes to "Sendai Marugoto Pass".http://www.sentabi.jp/marugoto/
Although the effective range etc are the same, I have not confirmed whether
there is a small difference or not about "Facilities Offering Special Benefits".
Depending on the progress of autumn leaves,
famous tourist spots such as Matsushima and Yamadera are also included.
At Matsushima's temple light up at night,http://www.miyagi-kankou.or.jp/tourist_infomation/en/
Yamadera needs to go up many stairs, but there are also hiking courses nearby.http://www.yamaderakankou.com/pamphlet/
Also, although can not go on this pass,
there is also "Naruko " as a daytrip for colored leaves close to Sendai is very famous.http://en.naruko.gr.jp/
If you are traveling with 'Japan Rail Pass' or 'JR-East Pass', you can use Shinkansen faster.
However, if you can get "IDP", rental car plan is more convenient for Jogi and AkiuOtaki.
There is no expressway(toll road) and no charged parking lot in both spots,
just a little expensive but the comfort is quite different.
Many locals come by own mortorcycle or sport bicycle as short touring.https://blogs.yahoo.co.jp/zenkoujimania/63850765.htmlhttps://ameblo.jp/munesan9483ame/entry-12282343616.html
You can not drive a motorcycle with IDP, but you can rent this sport type bicycle even in Sendai. https://giant-store.jp/giant-store-rentcycle/en/index.html
However, it is not suitable for beginner cyclists as it has a long distance and many slopes.http://www.brenda-bicycle.com/brendablog/?p=5341http://www.brenda-bicycle.com/brendablog/?p=5513