Do you prefer giving or receiving presents?

Completely different words.

Breaking down the words:

• 投 tóu: cast, throw
• 桃 táo: peach
• 报 bào: report
• 李 lǐ: plum

This sounds like gibberish because it is. Chinese characters aren't quite words, but are more like "roots" in English (like "bio" meaning "life"). As such they have broad and shifting meanings. The big two are the first word and the third. The first word literally means "throw" or "cast" (as in fishing line), but has other shades of meaning that imply "giving". The third word literally means "report" in most uses, but can also mean "repay" or "reciprocate". Factor into this that word forms and declensions just aren't a thing in Chinese, and this particular expression stems from the Book of Songs which is written in the very, very, very terse language of Classical Chinese and …

… well translation is shifty and difficult.

Another way to translate this (with implied meanings in [brackets]) could be: "toss [someone a] peach [and he will] reciprocate [with a] plum".

Or, you know, give a peach in return for a plum. (And my brain screwed up above which I will correct: I flipped plum and peach for some reason.)

As for the other part of your question, the characters for the online purchasing platform are: 淘宝. Breaking that down:

• 淘 táo: wash, cleanse, sift, eliminate
• 宝 bǎo: treasure, jewel

That first one is MOSTLY used to talk about sifting (such that 淘金 means "sift gold" or more idiomatically "pan for gold"). So the literal translation of that name is "sift treasure" or, more idiomatically, "treasure hunt".

Insert the "the more you know" meme right here. 😆