Panel 1: I wasn't sure who was talking at first, then I realized that the phrase "parental roof" most likely indicates Mike. (Although he goes easy on the pretentious writer talk in the strip; that's mostly in the letters.)
Panel 2: And there you have it, folks. She wants a boring suburban life, with a dead-looking stuffed animal belly-up on the kitchen table. At least the wine is out of her reach, though I'm sure by the time she's forty, she'll have learned to hide the empties in the cabinet where the water softener is and sneak them out to the trash bin in the dead of night.
Panel 3: Well, that answers one question. And she actually wants to pay more than they asked for? Perhaps the extra expense is worth it to her, if it's the price of avoiding real responsibility. Elly-face on Mike again, BTW.
Panel 4: Well, to quote Liz herself, this doesn't add up. If she really wants her business to be her business alone, $500 could probably get her a solo apartment quite easily. I mean, I do understand those narrowed eyes, but I don't think $5000 would be enough to keep Elly's potato nose out of her business if it really came to it.
That second panel really grinds my gears. There's no reasonable explanation for why this character did such a 180. She was all gung-ho to go up north and experience a different culture. Sure, she was homesick the second month she was in Mtig, but that can be worked through -- and that's what Shiimsa was supposed to help with. She was adjusting, she didn't seem to overly mind the gossipy nature of the community -- I mean, I know I would, but that's me, not Liz -- she had a boyfriend who adored her, Jesse was her pet project, and she was presented as being good at her job. Now, out of no-freakin'-where, she wants "dull". All I can figure is, this is a delayed reaction to, and the net result of not dealing with, the going-after. Because that's another way she seemed self-sufficient: operating the heavy machinery and giving good comebacks to Howard (at first). But then he became menacing, not just a pain in the ass, and since then, Liz has been retreating further and further, closer to the womb. Lynn, why are you doing this? You're the one who takes such pride in being the first female syndicated cartoonist, triumphing in a man's field and all that. So why are you making Liz into such a pushover?
ETA: Y'all have to check this animation of Thursday's strip, over at Comics Curmudgeon's message board: http://joshreads.com/forum/viewtopic.php?t=83&postdays=0&postorder=asc&start=1755&sid=bb7f13abd9c13412a4d99aa16357566d