I'm not all that familiar w/mesothelioma; but, anything that helps the immune system is good for any sort of cancer. The thing to watch out for is to go slowly enough to avoid herxheimer (the dead pathogens overloading the ability of the liver and kidneys to process them out of the body); but, to still hit the cancer hard enough to get ahead of it. Sort of a tight-rope... What I've found to be best is to just adjust the dosing to the individual. If all is going well, it can be bumped up a bit; but, if it seems like smaller or less frequent doses are needed to give his or her body more time to get rid of the dead pathogens, I back off a bit. I'm currently treating one of my fur-kids for GME that way; and, he's doing very well.
Give the MMS2 capsules by just getting them down his throat. Make sure that they're far enough down to be swallowed immediately; since, throat tissue is very tender and calcium hypochlorite is very alkaline. Get him to drink plenty of water right after each capsule, to make sure it's all the way down. If you're able to soak him in warm water, I'd also suggest soaking him in a bath of calcium hypochlorite and DMSO. (Not sure of your tub size; but, I put about a cup or a little less in a decent sized tub. A few drops of DMSO will help it to be drawn into his body. Although many people prefer to buy prefilled capsules for oral dosing, I generally just buy the 1 pound bags of it that are sold as pool shock; since, I use a lot of it as skin spray. It costs me around 4 USD for a pound of the stuff; and, Ortex is 68%. (Not sure if that brand is carried in Spain; but, I'm sure other brands carry 68%, as well.) Here in the US, DMSO can be bought at just about any feed or farm and ranch store pretty inexpensively, as well. If you can add soaking him, make sure it's in a well ventilated area.
I'm sure that others here can give you more thorough suggestions; but, I hope this helps some. To me, dogs are family members; and, if I can do anything to help one of them, I want to.
I forgot to mention that CH will out-gas in about 15 minutes; so, I'd mix/disolve it in a sealed bottle; then, pour it in after getting him into the tub water. MMS1 or CDS could be used, instead; but, since CH is so easy to come by (at least here in the US) I'd go with that for soaks; and, save the rest for dosing him orally.