I find the complaints about 10 yards really peculiar! At one point the teaching around here was the you don't step out the 10 yards because it looks amateurish. Just eyeball it.
I found that simply causes too many complaints - but it's absurd. Why do they think 10 steps = 10 yards? Bizarre!!
Anyway, to echo comments above, join your local RA if you haven't already. It sounds like you could do with some mentoring.
To address your specific incidents:
Anybody calling you a cheat should be taking an immediate trip to the carpark. Managers don't get to do that - and at this sort of level I'd be getting the managers to get rid of spectators doing that.
As for the manager coming down to argue with you.....I'd simply be advising him "You worry about coaching your players, I'll worry about the refereeing. Please return to your technical area - and any further dissent from you will result in you getting yourself sent from the field". This is really unacceptable behavior from the manager and with a bit more age and confidence you'll be able to handle this sort of appalling behavior much firmer.
With the manager in particular, once he starts dissenting, at the next stoppage you'll run over: "Manager, do you mind keeping a lid on those comments? I'm just calling it as I see it here". If he persists: "I've asked you earlier to stop the dissent and you've continued. The players wouldn't be getting away with this much on the field - so now I need to be clear. If you keep it up, you will be sent from the field of play".
Ask, Tell, Go. Next time, he's walking. If he doesn't, match is abandoned. You need to cut down on these managers early - otherwise they'll influence the players and you won't be able to control the match.
I've never sent off a manager and regretted it. But I have, on a number of times, regretted not sending off the manager - or not doing it earlier. At youth in particular, once a disruptive manager leaves the players tend to calm down.
You do not ever want to recount 10 yards. not for a manager, not for a player. You're undermining your own authority by doing this.
What I would suggest is at some point during the week, head out to your local field and step out the field markings. Centre spot to the edge of the centre circle is 10 yards, so pace it out. Try to make 10 steps get you to the end. From that you'll start to get a feel of the right step sizes - but if you do that a few times you'll learn.
You want to try to avoid doing it in 11 or 12 steps because then they'll complain that it's 12 yards. Makes no sense!
Finally, I'm going to go back to my comments about mentorship. I have a suspicion that you may not be portraying confidence on the field which is why the manager was all over you. As a young referee it can be difficult - the manager has probably been involved in the game for longer than you've been alive so he may well have trouble accepting your authority - yet you know more about the laws than he does. So look confident. Strong, confident arm signals. Walk tall, not hunched. Don't put the whistle to your mouth unless you're going to blow - and when you do, make it LOOOOUUUUDDDD. You want the players on the next field across to stop when you blow your whistle!!
And use your tongue. Do this (serious) - say, out loud, 'Toot'. Feel how the air starts and stops suddenly from your tongue? When you blow the whistle, do exactly that. If you put it to your mouth and just blow, it has a softer start/finish and just sounds weak.
Confidence stems from knowing the laws though. Make sure you know Law 11 and 12 in particular. Thoroughly. But with some mentorship you'll be able to see where you can improve.
Good luck and keep posting your queries on here!