Lock picks require a specific button for interaction. Starting out, you can only really pick locks in dungeons, but if you get lockpicking levelled up enough then you can elect to get into trespassing under the burglary skill branch, and it goes from there.
Cute mitts are available at the grocery store in uptown - pretty much all the options for presents are there in the current build, apart from sex toys (which are now found in the appropriate shop in Downtown's Digital Square).
To get two stars on a date, you need to get a kiss. Pick all the choices that make her happiest, then give her a gift that she's been looking for (desired gift rotates on Sundays in addition to changing after each gifting, so be wary of that). I usually just go for all those things and it'll secure the kiss each time.
For home dates, you need to manage lust and mood. The best way to boost mood is with a preferred food or beverage. Unfortunately there's no good way to figure this out beforehand, but you can come to a date with all the options to fish out the one she prefers (and since shops buy back at the full sell value, you can always sell back anything you don't want to keep for later).
Do keep in mind there is a bit of a "tire" mechanic, so leaning too hard on food or drink or just straight watching movies will come at a point of diminishing returns.
"Talk" will let you feel out how she's feeling. Gazing into your eyes means she has additional boosts to mood and lust, and biting her lip with a blush means she's ready for you to dive right in, even if she's not undressed.
That all said, I don't recommend going for a kiss until she's at least taken off her top. Sometimes it's actually just easier to go right to the climax and skip kissing depending on how high her lust is when going into the date, so keep that in mind too (feel like that might change in a future version but with the current 0.42 it still holds true).
