#1). YOur question reflects ignorance. I was there once and a nice gunsmith went over this with me, so let me "pass it along." Please.
#2). About anything can be done if you have enough money. ANYTHING. You suggest saving money. This limits things alot. The Swedes, for one example, were very strict about replacing barrels that started to show wear. SO, you can get Swede 96 barrels not too expensive, used or surplus unused, sometimes. Often, I am told, the Mauser standards were such that you could screw a barrel from one action into another similar action and it would headspace without fitting! Swede is pre 98 so you could screw a barrel into any "small ring" Mauser. '93. '94. '95. '96. And I think there were made some small ring 98's it might fit. So if you would be happy with a 6.5x55 rifle.
#3). My gunsmith friend had a left handed son. He got into Savages when that was all there was left handed. Loved them. Savage uses a newer barrel installation system. You might want to study on that.
#4). As said, I think this is correct but don't have manuals in front of me, Remington 700 uses a smaller thread and different pitch than a Mauser 98. A very good machinist could probably make a bushing to fit the smaller thread to the larger thread... You don't want to know what this sort of thing costs. Safe? Good question. Or "build up the Remington and recut the threads. This might involved re chambering. Again, bring money. LOTS!
#5). You suggest taking a "take off" barrel and screwing it into your gun to save money. Yes, there are take off barrels. Hit the largest gunsmith operations. Some people buy a whole rifle just for the action or action and stock and the barrel is removed carefully and sold, almost new, cheap. (Good place to start is the 'smiths listed on benchrest.com. Biggest and slowest...) If you can find a take off barrel for the action you have ["mini mauser"] then it should be fairly easy and safe and quick and ... Surplus 98 barrel? Again, not the way to "save" anything. Pay enough and it might get fitted. Now if the 98 is, say, 7x57 or 8x57... I doubt you will get the magazine in a mini mauser to feed that. You might have a single shot and you might not have enough steel.
Yes, this is a zoo. If you must, find a very good local machinist to advise you. You can save money if you do enough home work (and don't value your time...). But "run amok" and you might even hurt yourself, wallet and/or body. luck.