I have a toilet drain done, but when I flush the toilet, the water is not rushing down the bowl, but rather takes time to develop the spin. I am wondering if this is the right way to do it and use short 90degrees, rather than long turns
Two issues come to mind here.
First, I think the way your toilet is flushing is not related to the way your waste lines are plumbed. Unless you have another toilet of the same make and model that flushes differently, I think that's just how yours works. Even if your venting was nonexistent, your 4" waste line should have plenty of air space to let it work ok.
Second, I do think you have a problem with your waste line. I'm assuming the close vertical pipe is the drop from the WC? If so, the next fitting down, the Tee, needs to have a sweep. I found this answer elsewhere in stackexchange.