rail pass coverage

Hello,
So I'm planning to visit Japan this summer.I'm confused about purchasing the railway tickets. I want to make sure that the nationwide Jrpass offers all the descriptions mentioned in the regional passes. Is this right?

I mean, if I go to hakone and osaka,do I have to pay additional fees to use the trains and buses and offers that the regional passes include? Or my nationwide pass will cover those around city transportations mentioned?

Thank you for your time in advance

If you are going from Tokyo to Hakone, the part covered by the nationwide JR pass is from Tokyo to Odawara. The rest of transport "within" Hakone is not served by JR (Japan Railway) but Odakyu and other railway companies. So you might want to purchase Hakone Free Pass from Odawara to travel "within" Hakone.

Osaka: again it covers the Tokyo - Shin-Osaka - Osaka JR travel, and then the JR trains within Osaka.

To make it clear...

I want to make sure that the nationwide Jrpass offers all the descriptions mentioned in the regional passes. Is this right?

No. Just because something is covered by a regional JR Pass does not mean it's covered by the nationwide one. This is especially true of non-JR-operated lines, which are never covered by the nationwide pass with only one-and-a-half exception (the Tokyo Monorail and partially the Aoimori Railway), but also of some JR ones as well (the Nozomi shinkansen, which is covered by regional passes of JR West bt not by the nationwide one).