Hello mitra haru,
My TPS is still pending, but can I travel within USA or Canada by showing passport?

Yes, you can travel within USA with your passport. For domestic travels within USA, you only need to show an identification document, no valid visa or valid immigration status required.

To travel to Canada, you cannot. You need to have a Canadian visa first. Second, to return back to the US, you need an advance parole document, if your only immigration status is TPS. You can apply for advance parole (I-131) with pending TPS.

what about those who have a valid status (F-2 in my case). Applied TPS, which seems to be taking forever! I already got EAD but haven't used that to apply for SSN or work so technically I'm still F-2, right? I need to go home asap and don't think AP will arrive on time. So what happens if I travel without AP? Will I get in trouble on my way back at the POE? My F-2 visa will still be valid at that time.

Thanks

Get your documents to prove u need to visit nepal asap and goto local uscis office. If they believe u, they will issue u AP on the spot. If u travel without AP, u will still be on F2 and be able to return back but it will void ur TPS application because it proves u donot need protection anymore.

if you are not using AP, you need to have valid F2 visa in order to return back to US