Can someone explain?

1.Hayran olmak/kalmak,

and

2.to attract attention

Ilgi çekmek

Ilgi toplamak

Hayran    olmak  =   to   admire

I admire  your   enthusiasm for  learning   Turkish.

Senin  Türkçe  öğrenme  gayretine  hayranım.

Hayran   kalmak  is  more like  ‘to  be amazed at  something’,  ‘to be fascinated with  something ‘,  ‘  to  be  impressed  by something ‘

Onun   dansına    hayran  kaldım -à   I  was  amazed  at  his/her  dance [dancing]

ilgi  çekmek  -   to  draw  attention

ilgi   toplamak  -  to  arouse  interest,

Çocuk  annesinin ilgisini  çekmek  için ağlıyor -à  The child  is crying  in order  to  draw  his mother’s  attention.

Using  “toplamak” with  above  sentence would sound weird.

- Yönetmenin  yeni  filmi  büyük  ilgi   topladı.

 The  new  film  of   the [film] director  attracted  a lot  of  interest. [ in other words,  it [the film] was liked  by many people,  its sort of become  popular  among people,  it  attracted many people’s  interest on it,  it  aroused alot of  interest among people ]

Hope  it helps, may be someone else can explain better.

So can I say?

Türk diline, tarihine ve kulturuna hayran kaldım.

There is  idiomatic derived form of  " ilgi  toplamak"  which is  ---> "ilgisini   toplamak"  

"to being able to concentrate [focus] on  doing something....."

 Bir  türlü  derslere  ilgimi  toplayamıyorum.  ---> I can not  focus on studying. 

But  this is not a proper way ,  i mean "dikkatimi  toplayamıyorum" should be used instead.

Yes, you can. [ in past tense form]

But if you want to use "present tense", then it is better to say ; "hayranım"

Türk diline, tarihine ve kültürüne  hayranım. [ I admire..............]

ok

teşekkürler

Sorun  değil.

I need explanation about following verbs…

It would be nice if someone who is willing to explain to write sentences as examples.

Razı olmak

Razı gelmek

Razı etmek

The difference between "hayran olmak" and "hayran kalmak" is that the former one expresses a continued admiration over a long period of time, possibly for more than one achievement, while the latter indicates a sudden admiration, usually for a single achievement.

"ilgi çekmek" is usually getting attention of a limited number of witnesses at a given occassion , while "ilgi toplamak" is getting attention from a wider puplic, over a longer period of time, possibly for more than one achievement.

Razı olmak : to agree with something out of one´s free choice

Razı gelmek : to agree with something (probably because the circumstances leave no other choice)

Razı etmek : to get someone to agree with something, to persuade someone into an agreement.

tşkr AlphaF