Asked February 22, 2021, 5:26 PM EST
Travis County Texas
I cannot help you with questions about disposing of your broken pipes as this is not really a garden/plant related question.
With regard to your tree limbs, depending on their size there are several options:
1. Cut them up for firewood. If you do not have a fire place yourself, you can always strip off the leaves, cut the branches into sort of manageable lengths then post a "FREE FIREWOOD" post on your neighborhood website or Craigslist. I have done this in the past and when I had a lot of juniper I had cut down. People came by with trucks and hauled it off!
2. There are various services that pick up brush or bring over a chipper and chip in into mulch. The latter has the advantage of providing you with a very useable pile of mulch that you can apply to your plants and trees.
3. The city (as well as some private companies) have branch drop off sites. The city recycle centers will accept the brush at no cost. (Not sure if they are operating due to COVID). Private companies charge by the cubic yard - then mulch and resell the wood. The disadvantage of course is that you need to haul the wood to the center.
4. You may also want to talk to your trash pickup service. The service may offer some sort of brush pickup.
Last resort, is to just pile all the branches up and let them slowly breakdown. I do not recommend this option as it can take literally years for branches to break down, the pile will be unsightly, attract snakes and can also be a fire hazard in summer.
Travis County Master Gardener