First of all, that computer is honestly not much better than the one you have right now. You're better off buying a barebones computer kit and upgrading it as you have the money to do so. Why you even want a ZIP drive is beyond me... 100 Megs of storage is... pitiful compared to what your LG DVD burner can do. They make $10 flash drives that hold 1000 times more data than that thing. If it's for legacy support because you have life-altering data on the drive, just find an old USB model somewhere and use that instead, these modern boards don't support them very well anymore - if at all.
The other reason I suggest doing a barebones is that if you want 2GB of DDR RAM in the system, you're going to spend a pretty penny, since DDR is no longer made. You'll spend at least $47 buying the RAM when you can get 8GB
for the same price with a newer platform.
Windows XP is end of life. If you're using 98, and used to it, don't put it off any longer, get yourself up to Windows 7 level post-haste. Hell, even Windows 8 is on the horizon already. Vista was fine once SP1 came out, and SP2 really helped polish it out. I had some problems initially with Vista before either service pack, but SP2 and beyond was fine. Windows 7 strengthens that even further, it is totally what Vista should have been.
To answer your questions more directly,
1) ZIP drives were notorius for this. You need to have it on its own chain, without any other device to really get it to play nice. This kind of conflicting device issue is sooo 1998
2) The difference between DDR333 and 400 is price. You'll never notice the difference, DDR400 works fine in a system that was only supporting 333 at the time. As was the case back then, always buy the fastest and largest DIMM that the board supports. In this case, two 1GB DDR400 sticks would be fine. Just stick to name brands (the price I quoted above ($47) was using G.Skill DDR400 sticks at 1GB each on Newegg)
3) See above. XP is EOL (End of Life) and will soon be unsupported entirely. You're better off scrapping this system or donating it for a tax writeoff and buying a barebones PC kit. You can actually get them for as little as $150 if you know where to look (Includes Motherboard, CPU, and in some cases, RAM, power supply and case for about another $50-$80)
I just configured a new system on Newegg that has everything (except the OS) that would get you going, out the door for $272.94 if you're interested in it. There's nothing wrong with piecing it together as you have the money, I'd start with the smaller items and go from there, but I understand the bit about not having the money to upgrade to something newer, just trying to keep you in a forward moving direction.
Newegg.com - APEX SK-393-C Black Steel ATX Mid Tower Computer Case
Newegg.com - Antec NEO ECO 400C 400W Continuous Power ATX12V 2.3 / EPS12V 80 PLUS Certified Active PFC Power Supply
Newegg.com - GIGABYTE GA-78LMT-S2P AM3+ AMD 760G Micro ATX AMD Motherboard
Newegg.com - AMD Sempron 145 Sargas 2.8GHz Socket AM3 45W Single-Core Desktop Processor SDX145HBGMBOX
Newegg.com - G.SKILL NS 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10666) Desktop Memory Model F3-10666CL9D-4GBNS
Newegg.com - Western Digital Caviar Blue WD1600AAJB 160GB 7200 RPM 8MB Cache IDE Ultra ATA100 / ATA-6 3.5" Internal Hard Drive -Bare Drive
The hard drive is the most expensive component due to the flooding in Thailand right now, but if you ignore it, the entire price of the system drops signficiantly and by the time you get around to buying one, prices may have normalized. Without the HDD, the system is only $193. Not bad considering it would have 10x or more the processing power that the P4 would have.
The motherboard also has the video, LAN, sound chips already on it, so there's no need to buy those items separately.
Again, I understand if money is too tight, just trying to give you alternatives that you may not have considered before.