Is ability to easily pollinate desirable? In Mendel's crosses was it desirable for the plants to be able to cross-pollinate and self pollinate easily ?

Yes, the fact that pea plants were easy to pollinate was desirable and helpful in understanding the effects of Mendelian factors (genes) but for the proper study of the factors expressed CROSS POLLINATION of homozygous plants having different phenotype and genotype ( e.g. cross between RR and rr) was preffered rather than self pollination.