Why does the search for one of the ways to treat ceremorphosis cause disapproval among companions who are in favor of treatment, but in a different way?
If you mean Lae'zel, it's because she is a Githyanki, a race of interplanar warriors that considers itself superior to other races due to their vast collected knowledge and specializes in exterminating the mindflayers (ghaiks). Due to her studies she knows her people have a way to purify ceremorphosis, although she is quite secretive about it. So she sees any attempt at a cure other than her own as a waste of time and effort but most of all as mistrust against her and her knowledge.
If you mean Shadowheart with Auntie Ethel scenario, it's because she is being careful and does not think you should be sharing your condition with every single backstreet healer you come across. It's reckless and potentially dangerous.
Why is none of the companions trying to find out where we are (including the main character)? If we are close to a large city, then getting treatment there is much more likely than looking for help in the middle of nowhere.
They're not actually close to a big city and the issue is timing due to ceremorphosis.
They find out that Baldur's Gate is within ten days journey by foot, but there is plenty of danger on the way to it. And since classical ceremorphosis takes 7 days, they would never make it in time.
Why does Lae'zel act like she's tier 3 character (and why does she have a backstory like she is actually high level)? At the same time, she confesses that this is her first time on the continent and that we need to be careful.
It's the Githyanki ego. She considers herself vastly superior to you, which is quite obvious when she tells you; "You may as well suggest a wyvern bow to worms".
But in actual Githyanki hierarchy, she seems to be an aspiring novice, due to the way the kith'rak treated her. And also in her idle banter with Gale she mentions that she is not allowed to return home because she hasn't achieved anything of worth yet.
Where does she even get information about crèche? It could just be a group of Githyanki. They are raiders by nature and can use planar shift.
Lae'zel knows how the Githyanki operate when invading other planes, which involves following a certain protocol and establishing a creche nearby.
She gets the information that other Githyanki are in the area from the Tieflings while being stuck in the cage and then later confirmed by Zorru in the Grove. And considering the Nautiloid was chased by three dragon riders (kith'raks), it is a logical assumption that the Githyanki spotted nearby are none other than the same dragon riders. And also... Lae'zel gets extremely pissed off when the kith'rak went against protocol, so she seems to know about these things.
Why no one cares about Drow or Githyanki in your party?
I guess because all of them just came off a Nautiloid and got out of a very extreme life or death situation. Not to mention they all believe they will turn into mindflayers. So racism and other trivial thoughts don't really take precedence when life is on the line.
Except for Lae'zel, who is vocal about her racial observations in Faerun. Others though don't seem to care.