Rope length is a good point. I don't know what the maximum rise and fall of the locks on the Trent & Mersey are. If it were 12 feet for example, your ropes would need to be at least 24 feet. Don't go for the cheapest ropes! The amount of use they get can play very heck with your hands! Gloves are useful!
One other item I found very useful when coming into moorings etc was a DIY affair of a longish broom handle with a large wire loop (the galvanised stuff as used for fences etc) securely fastened to the end by a fine'ish drill through. Great for steadying the boat when coming alongside or even holding the boat whilst someone else opens a lock or lifts/swings a bridge! Make sure the loop is large enough to fit over bollards as well as mooring posts.
And, yes, you can pull the boat through almost any lock. I've yet to find one that I couldn't! The ladders can get very slippery with both water and general slimey muck. Occasionally some are damaged and rather wobbly! There was one at Fall Ings in Wakefield that was terryfying to climb!