I'm a heavy plate wearer, use 1h and shield sneaking around is not my playstyle, however there are two major quest lines that require me to steal stuff by stealth. The thalmor embassy one and the thieves guild in riften. Is it possible to complete these quests wearing plate armor and almost no specialization in sneaking?

Never tried, but I am a sneak-master in terms of skill if I may call me this way. Unfortunately the trollface sliding npcs are a quite annoying. BTW! XD

It's possible to sneak with clothes and no shoes OR simple shoes... but it's interesting to use the MUFFLE spell. You don't need to have skills in illusion to use this spell and it helps a lot, if you want to sneak.

Hope I could help!

Yes. You CAN just smash your way through the thalmor if you desire. The contact is just wary about you being caught because he'll likely get exposed and executed.

Same is true of many other "stealth" quests. Because of course, even a stealth-expert can get caught out now and then and spotted and you can't really terminate a quest line because of it. Worst case scenario is an NPC berates you for screwing up

according to the http://www.rarityguide.com/articles/articles/1032/1/Skyrim-Walkthrough-Part-9-Diplomatic-Immunity/Page1.html you dont have to sneak you can fight your way through

Thieves guild quest in Riften if you are refering to the first quest, even if you "fail" the quest because you are caught, it still completes

You'll want a good sneak just for the recruitment task for the Thieves Guild. Let alone some of the later quests which require sneaking around (and never killing) multiple guards and such. Although from what Ive read there are Perks in the Heavy Armor tree that should allow you to do this in your plate mail.