using a dynamic database name over a linked server

There two questions here.
I need to query tables over a linked server. The tables all have the following structure
with a number that is the month of the year.
things_1,things_2,things_3.... things_10,things_11,things_12

the basic sql used is of the form (things_n corresponds to 1-12 as above)
select a,b,c from remoteserver.database.dbo.things_n
where convert(char(12),local_time = convert(char(12),getdate()-1)
and item in('a','b','c','d','e','f','g')
order by local_time

I should add that each of the remote databases are quite large.

question 1
I guess that I could construct a dynamic sql based on the desired month particularly if it was local but is there a better method short of a list of If statements?

question 2
Admittedly I have tried a dynamic sql but can not get it to work

declare @sql nvarchar(4000),
             @tblname nvarchar(9)
select @m = 1
select @tblname = 'things_' + @m
set @sql = 'select a,b,c from remoteserver.database.dbo.[' + @tblname + ']
where convert(char(12),local_time = convert(char(12),getdate()-1)
and item in('a','b','c','d','e','f','g')
order by local_time'

Do you have an opinion or alternative for question 1?
What is the correct format for question 2?

thanks