No. No no no no no to all.
No you can't damage the frame - as long as you have the nut with the "turney thing" against the drop outs, unless the nut is stong enough for you to squash raw metal.
No to adjustable spanners (I won't even mention the "p" word), You'll bugger up the nuts every time and you can buy a proper spanner for about a quid that'll do you fine. And you can grip like a bastard with those "P things" and you will get 5% spanner force. And you'll slip and leave your knuckle flesh on the frame while you swear like a marine with VD. And you will shag the paint right up when you slip.
Just skip a pint once this week, go to a hardware store and buy a spanner - open one end, ring the other. Then get another one the same, as you need two, balanced against each other, to do a proper job. They will last you years of glorious trouble-free wrenching.