I think it's usually a condition of entry that you allow yourself to be searched on entering a football ground. In essence, it's part of the contract when you buy your ticket.
However, as I understand it a steward must ask your permission before conducting a search, must be of the same sex as you, and there should be another steward present and able to witness the search. You are allowed to refuse a search, and the steward is allowed to deny you entry if you do so.
As for searching children, I think that's a grey area. For accompanied children I think the steward would have to get the permission of the adult accompanying them, and if it was my children I think I'd be well within my rights to insist that any search that involved touching them could only be carried out by someone who could be clearly identified as having passed appropriate safeguarding procedures - e.g. CRB checks. I wouldn't refuse a search, I'd just insist that it was conducted under appropriate conditions and if the club couldn't match that then I'd expect to be granted entry.
As for forcing people through specific turnstiles, then that seems petty to me, and unnecessary given that all turnstiles seem to be able to accept any ticket and movement within the area below the seats is ample and uncontrolled for the most part. Long queues are flashpoints for anger and frustration, and it seems to me that human nature is generally to move on to find the next shortest queue which speeds up ingress overall and benefits everyone. When numbers are so low, it just seems like madness having these endless second checks and fussing about - perhaps if we were getting 30,000 I could understand it.