When I say "no further recommendations" is plural use of recommendations correct?

Solution 1:

For the meaning that applies in the present case this word is both countable and uncountable. This is the meaning in OALD, 2, repeated below for convenience.

[uncountable, countable] the act of telling somebody that something is good or useful or that somebody would be suitable for a particular job, etc.

You can therefore choose the uncountable option and add no s or choose the countable option, but then either an s is necessary or, for the singular, a slight modification (We don't have a further recommendation…).

The adverb "no" is not determining in the choice of using a plural form or a form without s. (ngram); however, if no s is used it might not be clear whether "recommendation" is countable or not; if the context in what precedes does not make that clear, one possibility is as good as the other.

Of course, this way of deciding whether to use s or not is valid for all such nouns; you only need to check the particular noun in OALD or some such dictionary that makes precise whether a noun is countable, uncountable, both, or else.