You should go for R.C.T of third molar & bridge should be done extending from first molar to third molar. No need for extracting impacted premolar, if it's paining you can go for R.C.T of premolar.On the other side,R.C.T can be done on broken tooth, but depends on x-ray, how much decayed it is.

I understand your dilemma! Ideally root canal treatment is always a better option than extraction because the tooth is salvaged for few more years providing service. However any attempt in root canal should be performed only if all other situations support a successful treatment. Third molars generally can be treated successfully except very few rare situations where its location or extensive decay pose a threat. You pointed out that you got your 2nd molar extracted so that itself imposes a greater importance on saving the 3rd molar somehow else bridging will not be a success. Although other forms of tooth replacement are there such as implants but all depends on what is the overall condition. If the 3rd molar can be treated successfully then capping it for support shouldn't be an issue with minor modification here and there depending on the discretion of the operator. As with other decayed teeth, it will be in your best interest to get them treated asap alas they might end up broken beyond repair. Also don't forget to maintain good oral hygiene from here on to avoid any such problems in future. Cheers !