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Sometimes the climbing rosebushes just need a bit of thinning out as they get so overgrown that the bush works too hard keeping all of its foliage going. Other times it may be that the soil, as well as the bush, need some nutrients that they are not getting. I do not know what you are currently feeding your rosebush, but would recommend using a good organic rose food that feeds both the soil and the bush itself. Make sure the bush is getting plenty of sun (6 to 8 hours per day) too. If something is blocking the sun or if you have had a cloudy season, the bloom production may be far less. Look for any signs of insect or disease damage that might be stressing the bush out too. Some insects will attack the buds early on and they just fall off and do not bloom.

This could be caused by any number of things. This article may help narrow it down: https://www.gardeningknowhow.com/plant-problems/environmental/plant-leaves-turn-yellow.htm

You can with some of them. Others just will not stay in the roundish shape and will send new growth out beyond the bounds you would like frequently. I have done it with a climber called Altissimo, beautiful big red blooms. It is a matter of wills sometimes I must admit! If you keep after it and keep the bush trimmed back, it may hold fairly well. With some climbers this will also cause a lack of blooms. With some of the older climbers you may well lose all the blooms as they bloom on the "old wood" or the last years growth. So pruning them back a lot will sacrifice blooms.

As some climbing rosebushes get older and taller, they tend to drop all the foliage at the bottom. This is what we call a bush being "leggy". Many folks plant some nice companion perennial flowering plants at the base of climbing roses and some taller hybrid tea and grandiflora rosebushes. That way we have colorful bloom smiles at the base and up around the top as well. The canes of these climbers act more like supply highways to the upper part of the bush and thus do not want to rob any of those nutrients getting to the upper parts. Kind of a neat action of nature really.

It sounds like a good plan. I would be very careful with the Round Up though, a little drift of spray will cause problems with the climbing roses. For the grass and such that are closer to the bushes, try mixing some Round Up in a can and brush it on lightly with a paintbrush. There is a soils amendment out there called Clay Buster that works very well to help break up clayey soils, I know because I deal with it too!! Also I prefer either a shredded wood mulch (natural cedar or brown colored) or 3/4 to 1 1/2 inch gravel. The bark likes to harbor some of the bad guy insects and I have had worse problems with bad molds and funguses using the bark.