Hello. First off... seems like you haven't watched any video tutorials as if you had, you probably would never have had to post this. Please check them out.
If your dropdowns are not working, then they are not setup correctly. Dropdowns, radio buttons, and checkbox fields have a setting called Selection Limits. For each value in the field, you must provide a selection limit. It is like a capacity check for each item in the dropdown. Once the limit is reached, that option no longer will show. 0 represents unlimited. So if you have 3 options in your dropdown and can have 50 people choose each one, your selection limit would be:
50|50|50
If this is not setup correctly, it will keep that field from working right.
You do not need to modify code to make radio buttons / checkboxes appear vertically. There is a parameter in the setup of the field "New Lines: Yes / No". Set it to Yes and each value will show on a "new line"... vertically. Described in the tooltip and the video.
For your sessions... if you make each one a separate event, then there will be a form for each one, yes. If you use Community Builder or JomSocial, you can have the form auto-populate the default fields from the user profiles (name, address, city, email, etc). That will make things easier for the end user.
However, I would set it up using custom fields. There is not a display of how many spots are still available in each, BUT you CAN set that limit as described above. Once the capacity for the session is hit, others won't see it as an option to select in their registration.
Thanks and hope this clears things up for you.