If I peel and chop beats, and submerge in vinegar, will they be safe to eat days later?

Why not just put them in a bag and in the fridge the way they are? They're root vegetables like potatoes.

No!! The only thing those beets are going to be is nasty. Just go online and find a simple recipe for what you need to do, be it pickle them, roast them, what ever. They are one of the easiest veggies to cook with and you can fine very simple recipes for them. 

They should be ok done this way, you may have to rinse them if you dont want the vinegary taste in your cooked beets.

Do you mean 'beets' as in the root vegetable or Beats the music ear buds ?

Basically you'd be pickling them and not in a good way.

Beets keep well in a fridge - for a REALLY long time.  

I think this would not only be a waste of effort you'd ruin a whole lotta beets.

If I had a whole lotta beets I MIGHT pickle some, but I'd follow a recipe and jar them up so they'd be ready for future consumption with no further effort.  

But I'm not really much of a fan of pickled vegetables and I would be much more likely to ROAST the beets, then refrigerate them for a week or freeze them for much longer.

I have two basic ways that I roast beets that I do a lot:

Peeled, cut into chunks, tossed with olive oil, garlic and herbs and roasted on a sheet pan (like roasted potatoes).  Roasted this way the sugars ooze out and caramelize and the beets become almost candy-like.  The first time I ever did this I was roasting a big sheet of mixed root vegetables and tossed some beets in for color.  My housemate and I sat there and devoured every beet on that platter as soon as they hit the table.  We started eating beets cooked like that ever night - our pee turned pink for weeks.

The other way is to scrub down the entire peel of the beet and let it dry, then wrap it in parchment paper (think like a hard candy with twisted ends) then bake at 350 til it's tender when you poke it with your finger.  Let them cool enough to handle them and when unwrapped the skin peels right off and you have lovely cooked beet for mashed beets, to make soup or pasta or just pile in a bowl with butter (or buttermilk) and seasonings (sweet OR savory) of your choice and eat with a spoon.  And these ones will make your pee pink too...

Yes, but why would you want to?  Whole raw beets keep really well in a cool dark place.  I usually have a dozen or so sitting in a clay pot in my pantry at any given time during the winter months.  If you're going to cook them it best to cook them with their skin on and then rub off the skin under the cold tap as soon as they're cold enough to juggle in your hands.  It's a fun job, but be careful, sometime they slip their skin and go shooting across the room!  Cooking them this way retains most vitamins and most color.  Beets are MUCH easier to cut once cooked.  Once cooked they keep for several days in a covered container in the fridge.  If you want to use them in a salad put them in a vinaigrette while still warm so that they absorb the most flavor, though move them to the fridge as soon as they begin to cool down.

i would hope so, just dont eat it if youre not sure

Yes. It's pickling, and an ancient form of preserving vegetables for the cold winter month. You don't need to cook a vegetable to pickle it, and the jarring process is only necessary if you're keeping things for months. Vinegar is a very good preservative. I often put raw vegetables in a pickling liquid - sometimes the left over liquid in a bottle of pickles, or sometimes a mixture I make myself- and the vegetables keep fine for a couple of weeks. You might find that pure vinegar makes them too sharp. A mixture with water, a little sugar, vinegar and some spices tastes best.