my thoughts as a learner .....

They are all reciprocal/co-operative verbs that can be used to mean ´to meet each other´. The slight differences can become clearer if you look at the root verbs.

Görmek = to see

Görüşmek = to see each other, to meet.

Ahmet ile görüşeceğim. I´ll meet with Ahmet

(Ahmet and I will see each other)

Different versions are often used in departure expressions

for example ´see you later´ = görüşürüz (we will see each other)

and görüşmek üzere 

Tanımak = to recognize

Tanışmak = to recognize each other, to meet for the first time

Used when you are about to meet someone or a group/family for the first time, or after meeting them. 

Tanıştığımıza memnun oldum = nice to meet you

Bulmak = to find

Buluşmak = to find each other, to meet (but you have met before this), and for arranged meetings

Seninle rüyalarımda buluşacağım = I´ll meet you in my dreams.

I hope this helps 

..... and there is also karşılaşmak

karşı = opposite, facing

karşılamak = to welcome, to react to

karşılaşmak = to meet, to run in to, to face each other, to oppose (for sports teams to play each other)

görüşmek = to see each other

konuşmak = to talk to one en another

So how do you see the other party when you are talking on the phone? I´m curious. Do you close your eyes and imagine his/her face?

And I´m also native speaker and it´s bad Turkish to me. Does not make sense to me. There are bad usages like that. You don´t have to speak like that. You can try to speak better Turkish. Not a problem for me if you don´t. It´s your problem.

"Görüşmek" verb´s other mean is "sharing opinions/ideas with someone"

Görüş: vision, opinion, idea - These are not physical, intangible means.

For example: "Bu konuyu görüştük"