HI Felix,
Try maintenance...
From the Safari Menu Bar, click Safari / Empty Cache. When you are done with that...
From the Safari Menu Bar, click Safari / Reset Safari. Select the top 5 buttons and click Reset.
If Safari unexpectedly quits, it could be a 3rd party plugins causing the problem. Go to ~/Library/Internet Plugins. Move any 3rd party plugins to the Trash and restart your Mac.
And make sure Safari is not running in Rosetta. Right or control click the Safari icon in your Applications folder then click Get Info. In the Get Info window click the black disclosure triangle so it faces down. Where you see Open using Rosetta... make sure that is NOT selected.
Try
Open DNS - Free / Basic
Go to ~/Library/Caches/com.apple.Safari/ Move the Cache.db file to the Trash and restart your Mac.
For Firefox:
1. From the Tools menu, select Clear Recent History... .
2. From the Time range to clear: drop-down menu, select the desired range; to clear your entire cache, select Everything.
3. Click the down arrow next to "Details" to choose what history elements to clear. Click Clear Now.
Repair disk permissions...
Quit any open applications/programs. Launch Disk Utility. (Applications/Utilities) Select MacintoshHD in the panel on the left, select the FirstAid tab. Click: Repair Disk Permissions. When it's finished from the Menu Bar, Quit Disk Utility and restart your Mac. If you see a long list of "messages" in the permissions window, it's ok. That can be ignored. As long as you see, "Permissions Repair Complete" when it's finished... you're done. Quit Disk Utility and restart your Mac.
Carolyn 🙂