As neighbors in a hostile region, they maintain trade agreements but keep to themselves as a general rule. Nevertheless, Elves do visit Laketown. It is doubtful that lake men visit the Elf King. They each value their Independence, and the Elf King is fond of their wine.
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No. There would be some reference to the Elves and Men mixing there. But there is not. They are separate races, and though they trade, they are not related.
In the Hobbit, King Thranduil of Mirkwood, the Wood Elves' king, liked his wine from Dorwinion. His wine was also imported by the Elves of Mirkwood in barrels down the Forest River from Long lake.
This question is difficult to answer, since they aren't always mentioned as individuals. In several scenes, we are simply told that elves were doing something, without being told how many. The number of elves at Rivendell is probably not all that great, since it is described as a single house (although presumably a large one). The wood elves are rather more numerous, sending an impressive army to the lake and the mountain after the dragon is slain.
They were tired and hungry with no food or water. At least with the elves, they were fed.Because they had lost their way in Mirkwood and were on the brink of starvation.
They took them to the halls of the Elven King in his hall, a large cave at the edge of Mirkwood. The wood elves of Mirkwood, in the Hobbit, took the thirteen dwarves to their king's halls, where they were locked in by cellars and a magic gate.