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

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.