Plumbing – Why multiple copper tubes joined together

You must have a vent. The toilet will not flush properly without one, and there will rarely be enough water left in the bowl. You need a 2" vent to take off from the branch line within 6 feet of the toilet. It can run up any convenient wall until it is above the toilet's flood level. Then it can run near horizontally (1/4" per foot) anywhere to tie into an equal or larger vent.

There's any number of ways to properly vent a toilet, and several common ways that are technically wrong, and even more that are just plain wrong. It's impossible to suggest a good method without a lot more information.

You have 3 shower heads on 1, 1/2" supply line The demand is higher than the 1/2" can supply. The size of the valves also makes a difference with high flow shower heads. Both the supply line and possibly the valve will need to be increased in size for full pressure with all 3 heads turned on. A booster pump or increase in pressure may be another option.