I have the Arena & Daggerfall self-extraction applications downloaded onto my laptop (which has a Linux operating system, rather than windows), but I can run em, instead it gives me a bunch of error messages.

They aren't Linux applications. The best way to set these up on Linux is to use DOSBox.

Arena is downloaded as a self-extracting exe. You can use unrar (and probably other unpackers) to unpack it.

Daggerfall is downloaded as a zip archive. You can use unzip (also unrar and other unpackers) to unpack it.

http://www.uesp.net/wiki/Daggerfall:Running_Under_DOSBox
http://www.uesp.net/wiki/General%3a%50laying_DOS_Installments_under_DOSBox

See instructions for installing Arena and Daggerfall in the second link.

Search the forum here, there have been a couple of good threads on running DF in Linux. I got it running very nicely from those.

tried searching, got like a thousand results.

Also tried using an unpacking program, still getting the sam error messages.

Arena error:

7-Zip 4.58 beta Copyright © 1999-2008 Igor Pavlov 2008-05-05
p7zip Version 4.58 (locale=en_US.UTF-8,Utf16=on,HugeFiles=on,1 CPU)

Processing archive: /home/mike/Desktop/Arena106.exe

Extracting ARENA/2651.GLD Unsupported Method
Extracting ARENA/39300577.MIF Unsupported Method
Extracting ARENA/39699021.MIF Unsupported Method
Extracting ARENA/39950681.MIF Unsupported Method
Extracting ARENA/40181409.MIF Unsupported Method
Extracting ARENA/40370128.MIF Unsupported Method
Extracting ARENA/40516921.MIF Unsupported Method
Extracting ARENA/40642738.MIF Unsupported Method
Extracting ARENA/40852494.MIF Unsupported Method
Extracting ARENA/41229981.MIF Unsupported Method
Extracting ARENA/41418704.MIF Unsupported Method
Extracting ARENA/41649375.MIF Unsupported Method
Extracting ARENA/42026882.MIF Unsupported Method
Extracting ARENA/42068779.MIF Unsupported Method
Extracting ARENA/42110737.MIF Unsupported Method
Extracting ARENA/42194658.MIF Unsupported Method
Extracting ARENA/42488253.MIF Unsupported Method
Extracting ARENA/A.EXE Unsupported Method
Extracting ARENA/ADLIBG.ADV Unsupported Method
Extracting ARENA/ALGDIG.ADV Unsupported Method
Extracting ARENA/ARENA.BAT Unsupported Method
Extracting ARENA/ARENAFNT.DAT Unsupported Method
Extracting ARENA/ARIADIG.ADV Unsupported Method
Extracting ARENA/ARIAXMID.ADV Unsupported Method
Extracting ARENA/Arrows.cif Unsupported Method
Extracting ARENA/ARTFACT1.DAT Unsupported Method
Extracting ARENA/ARTFACT2.DAT Unsupported Method
Extracting ARENA/AUTOMAP.00 Unsupported Method
Extracting ARENA/BOOTEXEC.CPY Unsupported Method
Extracting ARENA/BS5.MIF Unsupported Method
Extracting ARENA/CHAOSVSN.FLC Unsupported Method
Extracting ARENA/CHARFNT.DAT Unsupported Method
Extracting ARENA/CHARSHT.COL Unsupported Method
Extracting ARENA/CHARSPEL.DAT Unsupported Method
Extracting ARENA/CHARSPEL.IMG Unsupported Method
Extracting ARENA/CITYDATA.00 Unsupported Method
Extracting ARENA/CITYDATA.64 Unsupported Method
Extracting ARENA/CITYDATA.65 Unsupported Method
Extracting ARENA/CITYINTR Unsupported Method
Extracting ARENA/CITYTXT Unsupported Method
Extracting ARENA/CLASSES.DAT Unsupported Method
Extracting ARENA/CONFIG.CPY Unsupported Method
Extracting ARENA/Crystal3.inf Unsupported Method
Extracting ARENA/DAYTIME.COL Unsupported Method
Extracting ARENA/DISKS.BAK Unsupported Method
Extracting ARENA/Docs/Arena106 Setup.doc Unsupported Method
Extracting ARENA/Docs/Passwords.txt Unsupported Method
Extracting ARENA/Docs
Extracting ARENA/DREARY.COL Unsupported Method
Extracting ARENA/DUNGEON.TXT Unsupported Method
Extracting ARENA/END01.FLC Unsupported Method
Extracting ARENA/END02.FLC Unsupported Method
Extracting ARENA/EQUIP.DAT Unsupported Method
Extracting ARENA/EXTRA
Extracting ARENA/FOG.LGT Unsupported Method
Extracting ARENA/FOG.TXT Unsupported Method
Extracting ARENA/FONT4.DAT Unsupported Method
Extracting ARENA/FONT_A.DAT Unsupported Method
Extracting ARENA/FONT_B.DAT Unsupported Method
Extracting ARENA/FONT_C.DAT Unsupported Method
Extracting ARENA/FONT_D.DAT Unsupported Method
Extracting ARENA/FONT_S.DAT Unsupported Method
Extracting ARENA/GENMIDI.ADV Unsupported Method
Extracting ARENA/GF1DIGI.ADV Unsupported Method
Extracting ARENA/GF1MIDI.ADV Unsupported Method
Extracting ARENA/GLOBAL.BSA Unsupported Method

Sub items Errors: 64

Daggerfall error:

7-Zip 4.58 beta Copyright © 1999-2008 Igor Pavlov 2008-05-05
p7zip Version 4.58 (locale=en_US.UTF-8,Utf16=on,HugeFiles=on,1 CPU)

Error: /home/mike/Desktop/DFInstall.zip is not supported archive

Errors: 1

Sounds like you may have just gotten a corrupted download. Bethesda's servers svck, they mess up files all the time. Clear your internet cache and try again. I'm on linux, too (Ubuntu 8.04), and I haven't had a problem running or installing DF.

Debatable. DosBox is the simplest way to set them up, in that there are step-by-step instructions available, but it can be painfully slow unless you have a very fast computer. On my laptop Daggerfall is an unplayable slideshow in DosBox.

The best-performing approach is normally to use dosemu, which lets them run at native speed. Daggerfall runs like a dream in dosemu on the same laptop. The downside is that it can be a bit harder to set up, and there's less support available if something goes wrong. Sound can be particularly tricky. But once you've got dosemu running, installing Daggerfall in it is almost exactly the same as for DosBox: just make the downloaded data visible within the emulated environment, run the installer, and launch the game with "fall z.cfg" instead of "dagger".

Which of these is the "best" way depends on what you're after -- support or speed.