For the first game:

Move 3: Too slow. A common tactic is to approach the opposite corner on the same side.

Move 31: Often the descent is better than the hane, because it is sente and doesn't allow later forcing moves.

Moves 33 and 35: I don't like this trade. white's wall is left floating and the group white was attacking or containing is perfectly safe now. If white is going to play against the upper right corner, maybe approach from the top side, inducing black to defend the corner and then making a jump by the top right side white group natural.

Move 39: Consider taking the corner instead?

Moves 41-46: White's first move is kind of slow. The ensuing sequence by black is painful.

Move 47: This isn't an attack because black's group is alive already. If you want to grow the top side, this is fine, but it damages the floating white wall by inducing black to surround it more.

Through 54: Black didn't jump far enough so white can play out this way, which is good. However, the decision to make black strong earlier by not responding to the peep hurts now, as black is naturally pushed into the area where white wants to make territory.

After that, the endgame started. Usually in a handicap game, white wants to be gaining on black for the whole game, to catch up and pass black in the endgame. Here, though, most of the endgame was played with Black making large reductions in sente.

Overall, I think white played a little too solidly and then left himself with a weak group to take care of that let black reduce a lot of white's potential.

Here are my thoughts on the first game. I left final thoughts on the last move.

_________________
"You have to walk before you can run. Black 1 was a walking move.
I blushed inwardly to recall the ignorant thoughts that had gone through
my mind before, when I had not realized the true worth of Black 1."
-Kageyama Toshiro on proper moves

Generally moyoaji you don't make that hane with in your first variation, you extend instead. There is a lot of aji in the cut there.

Ah, true. I was playing the basic 3-3 invasion with a two-space low enclosure without considering the stone on the outside until the end. You are right, that cut becomes a headache for black even before the mistake I showed.

_________________
"You have to walk before you can run. Black 1 was a walking move.
I blushed inwardly to recall the ignorant thoughts that had gone through
my mind before, when I had not realized the true worth of Black 1."
-Kageyama Toshiro on proper moves

A few comments as a 4k player.

You actually played White in the first game pretty well. By move 50 or so you had good chances of winning. You started off playing slow, and you might not have done so well against a different style, but there is little to complain about in terms of giving handicaps. Your worst play in that regard was , allowing Black to connect his weak group with . Divide and conquer is a good go motto.

One go proverb to keep in mind is, The opponent's play is my play. You missed chances to take away a good move for the opponent by playing there yourself.

You also failed to make a diagonal play to the second line where the opponent also has such a play. That play is often called a double sente. It is much bigger than it looks.

A number of times you made the mistake of pushing from behind. That is usually the wrong thing to do. Get ahead if you can.

Several comments:

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Well, thank you very much Of course I am still learning the fundamentals, but nevertheless this bit of praise encourages me greatly. I was playing rather slow as White in that game, but I did not want to scare Black into stepping up things. So I played à la Shuusaku. I'll need to improve on the divide and conquer part. I thought all the time that the Black group on the right side in my game against AnnaLena was unkillable. Perhaps by attacking it, instead of aiming to kill it, I would've won the game?

If I were "nekomataya" in that game, how should I play? White was not making much of a mess of things at the beginning, so as Black I was able to increase my influence unmolested.

Well, giving a solid strategy for white in a handicap game is difficult, because it presupposes that white is stronger than black and will win by taking advantage of black's mistakes, where the same strategy against a player of white's strength would lose. If black plays perfectly, white should lose every time. I think there are two schools of thoughts on how white should play, though: The first is that white should play calmly and not leave weak groups dangling around as targets and patiently wait for black to make mistakes. The second school is that white should seek to complicate the game in a way that black is uncomfortable handling, since in a complicated fight, white's presumably superior reading should shine through.