How can i have mobile number

I am clueless how simcards work in japan. Are there no prepaid simcards? Only plan?

If i get those with data only, i will not have a mobile number?

Which is cheapest but good network? Sakura mobile, bic etc.?

you can buy a prepaid simcard.
The data only sim card has its number for data transfer such as e-mail and web surfing but you can't use it for voice communication.

Softbank offer prepaid SIM for short-term stay with voice and texting capability.

If you are a resident, you can get a Softbank Prepaid voice SIM And phone for as long as you recharge it (valid up to one year after last recharge)

If you are a non resident, you used to be able to get either SIM + phone, or sometimes just the SIM at Softbank Roppongi. I haven't done this for a while, but this was consistently doable about 2-3 years back.

My problem is i carry an iphone with me but it is sim locked. As much as possible i dont want to buy a new phone. Is there a mobile network here in japan that can unlock my phone for free so i can change it to their network? Thanks

You have a few options, have it unlocked free in your home country from your service provider, getting it unlocked other than your home country is impossible, or buy a unlocked phone, if that is not an option, use a sim from you home countries service provider and roam.

do mobile repair shops in akihibara have phone unlocking services? if yes, how much do you think for iphone 4?

Unlocking is not well known, there are some in japan, but not much, you probably have to google for them first.