Rock ID help x2 please?

[Portlis]

Hey guys, if anyone can help me figure these out it's you. I've got 2 pretty interesting specimens that I have guesses at, but I'm not confident on either.

#1. Found in landscaping rock around the cities. It's a pretty decent sized chunk and has what appears to be bark on one side and a glassy mineralized interior. Is it petrified wood?

#2. More at a loss on this one. Found on the south shore of Lake Superior on an agate hunting trip. Needless to say I was disappointed with the agate finds, but found this beauty instead. It's a decent sized specimen and particularly heavy. It weighs over 5 ounces. It's obviously some sort of mineral with traces of its basalt (I think?) matrix still in tact, but I'm not sure what the interior is. The pink and green, as well as where it was found, make me think it's Thomsonite, but it almost seems too large to be Thomsonite and it's also missing the more glassy appearance that Thomsonite seems to have. Maybe it's just so highly weathered that the glossy look has diminished? I don't know... definitely a fascinating piece though.

[DARK30]

Top one looks like wood. Next one no clue.