I'm not familiar with the Tascam (I use all PC) but if it is a mixer with mic inputs you can record to it then send your mixed files to the PC through your soundcard. The Soundblaster has a stereo 1/8" mini phono so you may need adaptors to do so.
You can use SF as a recorder or editor - yes. To RECORD on a PC you will still need a mic preamp. If you connect your mic directly to the mic input on the soundcard you will get poor results. This is why you will need a mic preamp (ART MP I think is the cheapest at $99) to get the signal strong enough to go into the line-in on the card. There are 3 miniplugs on the card...output , mic and line in.
To get anything decent you will need the preamp. Once you have the file recorded I THINK you could connect the output of the soundcard back to the Tascam. I say think because I have never tried it.
Keep in mind your soundcard is 16 bit vs 20 or 24 for a better card. I know this because I have the same card. I record this way and it does work but for a really good recording on a PC you need a good soundcard. Same goes if you send an audio signal from your Tascam to the PC...it will sound OK but not high quality.
I think there are editors (maybe SF XP) which are 70 -100 bucks but I have a better version. Those run several hundred bucks...
You can go to
www.sonicfoundry.com to down load a SF demo or you might try
www.hitsquad.com to try another type. There are several besides SF...Cool Edit is one of them. Try them and see what you like.
You can also do audio manipulations in multitrack software. I currently use Cakewalk Pro Audio but there are many out there...n-track
www.fastsoft.com and Protools can be used as well. Not sure the Protools website though - just seach Protools and find the site. There is a free version of Protools you can get.
I still would record on the Tascam and send that to the PC to clean-up w/ an editor or record directly to the PC and skip the Tascam. I do understand the limited budget thing though...
I'm getting ready to upgrade to a Digi 001 / Protools LE set up and record EVERYTHING to the PC. It has a 8 in 8 out breakout box and is 24 bit...BUT it's like $900. And it's MY preference AFTER I did all my homework. (zip ducks and waits for the wrath of sonusman...

)
Don't get too caught up in spending a lot of money until you really decide what you need. Search this board for info FIRST...many swear by mixers / outboard equipment and many by the PC route. Experiment with what you have and learn on it - then search, learn and consider all options.
I hope this helps.
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