Toilet is not draining, and when plunged it backs up into the tub. Also water is coming out around the base of the toilet.

Sounds like you have a major blockage. Could be as simple as taking off the toilet and looking something physically blocking it, or something further down the drainage line. Look for a good plumber.

Your clog may not be major but it is downstream of where the tub and toilet drain connect to a main. Try removing the tub over flow cap and rod down through there, you need to get at lease 15' of snake down the vent. PS stop plunging, that works best when the clog is actually in the toilet or bend