Yes, when you add any two even numbers, the result is always an even number.
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No. because odd numbers don't have 2 as a factor but even numbers do. So it won't be a whole number.
The first 100 even numbers are: 2 468101214161820222426283032343638404244464850525456586062646668707274767880828486889092949698100102104106108110112114116118120122124126128130132134136138140142144146148150152154156158160162164166168170172174176178180182184186188190192194196198200.
Consecutive even numbers are any even numbers which are separated by one (uneven) number... so that 6 and 8 are consecutive even numbers... as are 22, 24 and 26. Similarly, consecutive odd numbers are numbers which are separated by one (even) number... so that 11 and 13 are consecutive odd numbers... as are 31, 33 and 35.
They can be integers, rational numbers or even approximations for irrational numbers.
If the average of 3 numbers is 37 then the sum of those numbers = 37 * 3 = 111. Which is an odd number. Adding together even numbers never results in an odd number. Therefore the 3 numbers can not be even numbers; consecutive or otherwise. The question can not be answered.