Can I stop Linux Mint from asking for my password when I install apps?

Automatic login and administrator authorization are separate things. Logging in gets you into your account, while installing system software or changing certain settings requires elevated privileges.

You can configure sudo to allow commands without a password, but that weakens a useful security barrier. A program or script running under your account could then potentially use sudo to gain root access without asking you. Being the only person using the laptop doesn't remove that risk.

For terminal commands, passwordless sudo is configurable through the sudoers file. Use visudo rather than editing the file directly, since it checks the configuration for errors before saving. You can set an editor with a command such as sudo EDITOR=nano visudo.

That only addresses sudo authorization. Graphical prompts can use a separate authorization mechanism, so changing sudoers won't necessarily disable every prompt. I'd avoid granting passwordless access to every command unless you understand the security tradeoff.

If the long password is the annoying part, consider changing it to something easier to type rather than removing the authorization check entirely. Pick something you can remember and type comfortably while still considering who might get access to the laptop.

It may help to note which app is asking and when. A prompt during installation is different from one that appears whenever an already installed app starts, so disabling system-wide authorization could be overkill for a single troublesome app.