Here’s my complete answers for you, though these are just my opinion:
1. With a tablet, you are better able to control details on texture that feel more organic. One good example is scratches and scars on a diffuse map for on a character’s face, which can look rather rigid if you use a mouse in trying to create (unless you’re just that good with a mouse, but still, it’s a whole lot more natural and easier to use a tablet). A tablet not only makes the creation process feel a whole lot better, but it also can save you a lot of time (how many times have you had to redraw that letter “P” on a sign texture with a mouse? Get it done once with a natural pen tablet). Though, a bit of a caution: when you buy a tablet, don’t expect it to be exactly like drawing with a real pen–it’s not a true 1:1 experience to actual pens, for the most part.
Basically, it’s a tool that offers to mimic a wide variety of tools, including pens, pencils, markers, charcoals, etc., and as such a universal tool, it’s got its own bit of a learning curve. It’s truly a tool of its own class, has its own feel, and may take a little time to adjust to using a tablet pen (and it might even take a little tweaking of the settings to get it just right for you). Perhaps the greatest advantage to a tablet is being able to express broad brush strokes or arm movements, even on a smaller tablet. The hand’s in a much more natural position for drawing forms with your arm with you need it. Speaking of hand position, the pen tablet is much more ergonomic than a mouse in painting textures, and you’ll feel that better relief on your wrist immediately. Once you get used to using it, and you’ll start to get a pretty good feel for it after about an hour or two, you’ll probably wonder how you ever did without it.
2. I personally use my tablet pen in a variety of ways in context to texture painting, but to give some examples, I often use the pen tablet as an airbrush in my painting program to get basic general areas covered and depending what it is I’m actually trying to create as a texture, I’ll use masks to act like stencils for my virtual airbrush and then use a fine brush to act as a fine-tipped paintbrush for finer detail (and this is one area where the pen tablet truly shines). Sometimes I use my eraser tip on my stylus pen set as another brush setting that I frequent use (many pen tablets come with an pressure-sensitive eraser tip). It’s really up to you how you use your pen tablet for creating textures, but it all feels much more natural than with a mouse.
3. Yes, I can say that a pen tablet will definitely make life easier for you–even if you’d still prefer the mouse for some things. Once you go with a pen tablet, it just becomes second-nature to you, and you’ll find plenty of ways to make it useful for you without even thinking about it. Again, there’s simply no match to a pen tablet in terms of a means that gives you the closer feel of working in natural media.
Are there alternatives? Yes, there are. In fact, I’d say that your best option is options. I myself still use the mouse for some things (especially when I purposely want that mouse-drawn look), sometimes I use the controllability of Bézier curves to perform curve-based operations such as stroking lines and creating outlines (which I tend to use the mouse more than my pen, but I do sometimes use my pen for that), and sometimes I use imported stuff such as scanning in an image or using a royalty-free texture from a website (which I sometimes edit using my pen tablet) as the base of some of my operations. The beautiful about using a pen tablet in your workflow is that even with the pen tablet plugged in, you can always just put it down and use your mouse when you need it.
4. Right off the back, I’m personally going to recommend the Wacom brand of pen tablets, which are undoubtedly the most popular and trusted brand, and also since I own one, though I’ve heard some good reviews about Genius brand tablets. As it seems you’re not looking for a whole lot more demand from your tablet as in doing other things than just texture painting, and I don’t know what kind of a budget you’re dealing with, I would recommend you check out the Wacom Bamboo series, specifically the Bamboo Create priced at $199 USD. Bamboo Create features 1024 levels of pressure sensitivity, multi-touch input (touch the pad with your finger in conjunction of using the pen to perform common commands), feel pretty natural to draw on, has more work area than the smaller Bamboo Capture (priced at $99 USD), and should be more than sufficient for your texture-painting needs.
Other brands such as Genius might offer you a good deal for less (such as the MousePen M508, which is a pretty nice tablet for $79 USD). If you’re wondering I many prefer Wacom, it’s because of their patented pen stylus technology that is always cordless, battery-free, available with tablet models that feature up to 2048 levels of pressure (the standard’s at 1024 levels), and uses a slimmer contoured pen stylus design. It’s up to you on what’s sufficient for you, and sometimes you can find any of these tablets at discounted prices with shopping online. Though, I say, if you are considering and willing to get a Wacom Bamboo Create at $199 USD, you’d might as well bargain for the even better Wacom Intuos4 Small tablet priced at $229 USD, which for about $30 USD more, you can have 6 fully-customizable ExpressKeys and a handy TouchRing which I constantly use with mine.
I hope this wasn’t too long for you, and I sincerely hope this helps! Cheers!