I'm no expert but I have successfully installed and used OpenBSD on a T420 and T430s, so I'll try my best to help.
Are you logging in via xdm or the console? If it's xdm you need to edit .xsession not .xinitrc.
In your xsession (or xinitrc) you should only need:
feh --bg-scale /path/to/image
I don't have a good explanation about your browser issue, sorry. Which browser is it?
The official OpenBSD FAQ and the man pages are always up to date. They have pretty much all the info you need to get up and running:
Here's a couple of blogs I always go to that should answer your questions. For OBSD official documentation is recommended, but I can vouch for these two sites:
https://www.c0ffee.net/blog/openbsd-on-a-laptop/ This blog hasn't been updated, but the info is still good. Also has relevant info about configuration on a laptop specifcially
https://sohcahtoa.org.uk/openbsd.html This one is updated with each new release
For wifi, as mentioned in the FAQs and the above blogs:
You need to create a file based on what type of wifi device you have. Since it's a thinkpad, it's most likely iwn0. Create /etc/hostname.iwn0 and add:
join "YOUR_SSID" wpakey "YOUR_PASSPHRASE"
Then run the following commands:
ifconfig em0 down
ifconfig iwn0 down
Wifi should connect automatically now.
For powersaving maybe apm is what you are looking for:
Hope I was of some help