2. At one point, Martha describes the Master as "immortal". This suggests that she's aware that Time Lords can regenrate indefinitely.
No, Martha never describes the Master as immortal. While explaining to Tom Milligan and Professor Docherty that she's looking for a way to kill the Master, Milligan waves his gun in the air and says that would do the trick. Martha then explains that it wouldn't since the Master would just regenerate, to which Docherty comments "great, he's immortal." Clearly, Docherty is just making a guess based on the info that's just been revealed to her, and at no time in this coversation does Martha or really anyone actually establish that the Master or any Time Lord are truly immortal.