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As far as I know all countries pay an entry fee to the contest which presumably is the same for all countries. However Spain, Germany, France and the UK as four of the so called “Big five” are allowed automatic qualification to the final because thEy are the 4 major financial contributors to the EBU. The fifth member of the big five, Italy, also gets automatic qualification, for reasons that aren’t entirely clear but probably partly due to their also being a big contributor and in an attempt to placate them after they effectively did what some here would like and went off in a huff for a few years. I think Turkey did the same thing for a while in protest at the alleged privileges afforded :-)
The contest like it or not is wildly popular in the UK. With so many participating countries now the likelihood of any one country winning is much smaller. One reason the UK struggles is that the songs it chooses are not really the sort of thing that’ll catch on in an evening and I suspect there is some displeasure that the UK which has such a fabulous popular music tradition continually puts up frankly second rate performers.
Many of the winning entries will have been played for weeks in advance in some countries, and often the performer is a household name in a lot of countries. In 2012 the Swedish entry could be heard it seems in every bar and cafe and not surprisingly won easily.