Does the order the queries are executed make a difference?
No, they reach for different things. The count will read a field that contains the number of colums of the table, the select by id will use the index. Both are fast and simple.
Is there a single query that will do what I want?
Yes, but it will make your code less clear, less maintenable (due to mixing concepts) and in the best case will not improve the performance (probably it will make it worse).
If you really really want to group them somehow, create a stored procedure, but unless you use this pair of queries a lot or in several places of the code, it can be an overkill.