There are tweet ads, yes. They are usually marked as "promoted"
I found it useful to "report as spam" the account they were coming from so at least you only see them once...
I found the new layout to be headache inducing for my english-speaking, left-to right-reading brain so I switched to the Chrome plug-in Silverbird on TVGugs recommendation... and haven't seen the promoted tweets since. Maybe that's because I'm using lists more... but it solved a lot of problems for me.
I take it Gmail has given out a bunch more invites in addition to the initial 5 or so they gave out with each new sign-up? Is that a sign of desperation, or a (late) response to how hot these things were a few months ago?