Yeah, they are grammatically fine. i really like your word order in a couple.
In the first you could use the more idiomatic construction of "they reached home awaiting their friends" in stead of introducing a comparative clause. i.e. domum amicos exspectantes advenirent.
Maybe if you wanted to make the sentence more Ciceronian, you could say 'agros transversos tam celeriter cuccurrer(e/unt) ut...' since, as far as i know, he didn't use trans.
(2) was great!
in (3) it may have been nice to reverse the order of the past participle and form of sum, perhaps ending with 'essent deletae' for emphasis.
In (4) I haven't seen auxilium parare before, in the sense of getting (non-military) help. Perhaps '(alicuius) opem implorare' may have been more idiomatic. I think, too, that 'adeo' should be used instead of 'tam' as it is the extent of the verb itself that introduces the consecutive/result clause. I think in the second half a demonstrative might have to be added to correspond to the relative. I always find it hard when you have little hidden relative clauses, but I think it should be written as "they ran as quickly as possible to the place from where they might...", which would mean slipping something like eo/illuc and then unde, so:
ut quam eo celerrime unde eam implorarent currerent.
(5) is v nice.
(6) I was sceptical about 'fieri potest ut' - as i thought it was a Late Latin thing of Augustine - but (the divine) Sir Mountford's Bradley's Arnold put me in my place. Nice! plus doloris has the partitive genitive and is formed correctly, but seems to jar for me, I think it is because patior is left without an object...maybe plurem dolorem would be more correct. i need to look into that one. And, a stickier subject still, but it is likely that the present subjunctive would be used after the quam.
But these are all minor points.