Those are not double verbs. Those are single verbs with an object or a prepositional phrase.
bás a fháil literally means ‘to get death’,
bás ‘death’ is a noun serving as an object of the verb ‘to get’.
dearmad a dhéanamh means ‘to make a forgetting’ (and what you wrote,
déan dearmad is imperative: ‘forget!’, ‘make forgetting’), the noun
dearmad ‘mistake, forgetting’ is an object. By the way, there also is a transitive verb
dearmad, and
Foclóir Gaeilge-Béarla even gives an example Dhearmad sé na pinginí, ‘he overlooked, omitted, the pence’.
If you conjugate (put in a given grammatical tense or person) a verb, you only conjugate the verb (not its object), hence
rinne mé dearmad, as
rinne is the past tense indicative form of
déan. The same wih
fuair sí bás, lit ‘she died, she got death’ – the only verb there is
fuair ‘got’, which is a past tense of
faigh ‘get’. You cannot say something like ‘*she deathed’ in English, because ‘death’ is not a verb, and the same way you cannot say
*bhás sí in Irish.
As for
cuir rud éigin ar ceal, it is a phrase, literally meaning ‘put something on concealment’, and less literally ‘cancel, abolish something’. Like in English you can ‘put up with sb’ and you cannot say eg. ‘*I was upping-withing him’ for ‘I was putting up with him' – you conjugate the verb part of the phrase. Or ‘write something down’ – you don’t ‘*down’ it, ‘down’ here is only an adverb, the only verb there is ‘write’.
EDIT: I wrote there is no verb ‘to die’ in Irish, but edited it now, as Labhrás pointed out,
básaigh exists, which without object means ‘to die’ and with an object ‘to kill’. Also, it is pretty common in Irish for nouns to have a corresponding verb ending in -(a)igh.