Will low C be as hard as Bb to play even though it is not a pedal tone?
Are pedal tones easier to play on large bore?
Kind of, but not to an important degree
Can you get luscious pedal tones down to E1 (no trigger) with a large bore tenor, or do you need a bass?
Depends on your definition of luscious, but listen to Joe Alessi play them on tenor
Pedal tones from trigger F down to C, compare large bore tenor to bass
Same as above, but mostly absent from tenor trombone literature
Practice both ends of the range, play the instrument you want to play, don't choose the instrument based on notes you want to play.
I'm sure you already understand that the bass, small-, and large-bore tenor trombones all play in the same key because the tubing is the same length. Where they differ is in bore size and extra "features" like attachment triggers.
For starters, any time you compare two instruments with the same length of tubing, the lower notes are going to be easier to play on the one with the larger bore. That's just physics at work. However, the pedal tones as they are known are the fundamental notes of the harmonic series that the trombone plays in. For this reason, the pedal Bb is one of the easiest low notes to play on trombone, regardless of bore size!!! A middle schooler with a small-bore instrument can play a pedal Bb if they approach it with the right technique. If you are still having trouble with pedal Bb on the small-bore, buying a larger instrument is not going to help you at all, and will probably make things a lot harder.
That said, if you are still using the stupid tiny 11C/7C mouthpiece that comes with most small-bore trombones, I highly recommend switching to something that will give you a little more breathing room. The only professionals that use mouthpieces of that size are jazz players that need to spend all of their time in the stratosphere. For all-around playing on the small bore, I recommend a Bach 6 1/2 AL small shank.
The low trigger range of F2 to C2 is actually an extension of the non-trigger range from Bb2 to E2. C2 is actually MUCH more difficult to play than Bb1, because even though the notes are only a whole tone away, Bb1 is a pedal tone played with the shortest possible tubing length, and C2 is a 2nd harmonic played with the longest possible tubing length, with the trigger activated and the slide out beyond 7th position (remember the positions get farther apart the lower you go).
The low trigger range is definitely in the large-bore tenor player's toolbox, and he or she has to spend considerable time working on it. The sub-basement below the G1 pedal tone is generally left to bass trombone players, though tenor players can and should practice them since working on both extremes of the playing range improves the facility with the less extreme ranges.
If you want to hear some truly luscious low range on the tenor trombone, listen to Joe Alessi (one example that is coming to mind is his performance of John Mackey's "Harvest" concerto, right near the 6 minute mark... a truly scintillating C2). Alessi is known for playing on very large mouthpieces, and it's been my experience that these can really open up the low trigger range for a tenor trombonist. However, any equipment size change is going to have a tradeoff with endurance or facility in the opposite end of the range.
Working on both extremes is advisable. Learning how to relax in the right way to play the lower notes will help you relax more in the middle and upper ranges. Exercising the high range is muscle-building, and should always be followed by playing some pedal tones to relax.
Another great exercise in the low range is to play false tones that don't actually exist on your instrument. With well-enough developed embouchure control, you can play F2 to C2 (notes that normally require a trigger) on a small-bore instrument. They're not going to sound the same, and you won't perform them, but they are good practice. Likewise, you can attempt "double pedal tones" like Bb0 without a trigger.
Like I mentioned before, larger instruments do make the high range more difficult, but Ab4 is not beyond the realm of possibility for a bass trombone player. Professional bass trombone players may practice all the way up to F5, but the highest that will reasonably be asked of them will be around Ab4 or Bb4.
You can already go broke buying mouthpieces, so I wouldn't advise buying different trombones just to expand your range. You should buy the trombone that you would like to play. If you're into jazz, or like playing with your local community band, or have a ska band or something, I can't see why you'd need more than a small or medium-small bore trombone. If you want to play big symphonic music, join an orchestra, play all the newest trombone solos, or study trombone at a conservatory, then you'll need the large bore tenor (and about 5 years to learn to play the damn thing). If you want to play bass trombone and hang out in tuba range all day long, buy a bass trombone!
After all that, it could just be that you need a larger mouthpiece, but that's something a private teacher would have to advise you on for a reliable diagnosis.