Honestly, you can just ignore them and progress through the main story (most of them will retrigger anyway). 

However, it's better to do TLQS. Not only it's an easy way to raise your stats and experience (you want to have high enough stats to unlock all dialogue options in main story), they also often give you tappies (more energy). Also, at least in my opinion, many TLQS are far more interesting and better written than the main story (which for me is pretty meh) - not all of them, sure, but many

JC put a lot of the new TLSQ in Y3 and to bring a little variation adds a few in Y2. Most TLSQ have a trigger chapter and if you progress in the story after triggering one you can create a backlog. Some of those quests are seasonal and that will lead to new(er) players having a string of TLSQ when JC triggers those TLSQ in their respective seasons (mainly Halloween and Christmas - yes, there are more Halloween and Christmas Quests than school years - ask JC what their reasoning is).

Here's a TLSQ Spreadsheet that lists trigger chapters, availability, and further requirements. Most quests will be available again - except the Quidditch TLSQ that are one try only.

It means you have a backlog of them. I had back to back for about two months, and then they slowed down, but they still give me one every 12 hours. I kind of wish they would wait at least 24 so I can make some progress in the main story.

I mean, it kind of is the game. If your intent is to do all of the TLSQ’s, the main story is definitely going to go on the back burner. I’m towards the end of Year 3 and the main story feels like a complete afterthought with how many TLSQ’s there are.

The game gives you 18-24 hours in-between triggering TLSQ’s though, if you’re getting back to back it means that a brand new TLSQ (that you’re obviously eligible for) was released while you were in the middle of one. Outside of a bug, I’m pretty sure that’s the only time they trigger back to back.

It's all story so my recommendation is just keep doing the TLSQs until they are done then you can get back to the main quest. You'll eventually reach a blocker anyways where the developers haven't finished the story yet and you're just waiting, and some parts you'll want higher attributes anyways which the TLSQs help you boost your attributes. Might as well just do these short story quests as they come up instead of rushing the main story quest.

As a person who has played this game multiple times (quit multiple times), I just do research on the TLSQs and just do the ones that interest me. If the rewards are boring for me or I don't get to interact with the character I wanna date, I don't do the TLSQ.

It all comes down to personal preference.

Well, year 2 has only a few TLSQs that you can actually play, so I would recommend completing them. If you click on your profile-) setting-) support-) help-) scroll down a bit, then click on "List of special adventures& when they start", you can check which chapters has what TLSQs, BUT if I remember well "The Weird Sisters" is in the memory book and you can buy it with pages OR JC is sometimes triggering it and if you don't want to spend pages on it, then you can just wait for them to trigger it. "Hosting The Beauxbatons"& "Son of Durmstrang" are not triggering when you reach their chapters, they are only triggered by JC at some point and you can do it doesn't matter if you are in year 3 or even above that. "Andromeda's Home Coming", "A Day In Diagon Alley" and "New Arrivals" are listed under year 2, but are actually triggering at the beginning of year 3 (because they take place on August 30 and September 1st in your 3rd year). If I remember well the club challenges are also triggered by JC at some point, so you can just move on (if I see it well only The Spinx Club challenge is listed under year 2 though🤔). For the Quidditch ones: You can start it in year 2 if you want to, but you can complete the 4 season whenever you want during your Hogwarts years (you SHOULD always do the Quidditch ones when they are triggering, because you have only ONE chance to complete them [you can Google Hogwarts mystery quidditch and check Hogwarts Cafe's walkthrough of each season to see when will the TLSQs trigger). Also, there are a couple of Halloween and Christmas TLSQs that are seasonal, and if you didn't already play last October& December to complete them, then you have to wait. So yeah, I would recommend doing the year 2 ones, since year 3 has a LOT more TLSQ and it would be like hell if you didn't do them while being in their year.