no, tn is not dual intent. you'd need to switch to H1B in-between.
It's possible. My opinion: just do it. If you were born in Canada/ROW, you need to plan it carefully (talk to your lawyer). If you were born in India or China, it's even more important to get your I-140 filed ASAP; with the proper strategy, the I-140 shouldn't prevent you from renewing TN status, but you should also be trying every year to switch to H-1B, as it does make things much easier.
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at what point is the TN status holder stuck in the USA? is it for the entire roughly 2 years that it takes for the eb-3 process? or only after filing a certain form?
Once you filed i485 you can also file for advance parole (form 130 or 131, dont remember). You will receive it in 6 month after application. I think you will get gc before AD expires. So, in short, your are not allowed to leave the US during 6 month period only (given you filed for AD).