Is the Shinkansen a “buy ahead of time so you don’t face a sold out tickets issue” type of line?

Super awkward wording of the title I apologize. Please be gentle and respectful or just don’t reply.

I’m travelling to Japan tomorrow with my husband and I’ve done a lot of research on passes and transport and as a result I’ve decided to use a suica card and conventional tickets as opposed to the JR Pass. What I want to know are these two things:

1. If I just go to a station to use the Shinkansen is there a likelihood that I’ll be screwed because I didn’t get a ticket ahead of time? Do the tickets sell out?
2. My understanding is that you can’t use the suica card to pay for the Shinkansen but I’ve gone over the wiki and other threads on this Reddit page and people are using a ticket AND the suica card? Can someone clear that up for me please?

EDIT; thank you so much for all the tips! Super helpful!!