Ableton Live you say? i'm aware of there software, but i've never done the research on it. speak on it.
Since it sounds like you're a "sample" based producer I'll hit you off with info. tailored for that.
1) Timestretching - is basically done automatically! As soon as you place the sample into your project by way of inserting it into a clip it is sync'd to the tempo of your project "automatically". If you want to "fine tune" your time stretching you have "5" methods. You can do so by beats,tones,textures,re-pitch and complex. You would choose which method according to the sample. For example, if it's just a beat (drum pattern) use beats for the best stretch. If it's a piece of an entire song with all the instrumentation use complex. If it's just vocals use re-pitch. Outside of choose with method you do nothing else.
2) Want to slice/chop that sample up? SUPER EASY! Click on the sample and you'll see everything about it at the bottom portion of your screen. You'll see the samples original tempo (now this is magic, when I sample I match my project tempo to the sample). You can set the time signature,swing,transpose, detune,sample quality (hi-Q for best results), volume,length of sample. Here you can see where to place your chop markers. Click on a marker and move it accordingly to set your hit points. Double click and it'll turn yellow. Chop marker is set. Right click on the sample in the clip view and scroll down to "slice to midi track". Now you'll have 7 slicing options, by marker,bar, 1/2 note,1/4 note,1/8 note,16th note or 32nd note.
Now if you want to get even more creative you can choose a sample preset. If you want the sample to stutter chose chord & stutter. There are 5 other presets to chose from. Shit will take your sample game to another level.
I'm tired of typing homie..lol. Get the demo and fuck with it. I promise you'll be hooked!