How can i fix my leaking toilet?

I live in an apartment and my neigbour directly below me came to speak to me about a stain that has appeared on his ceiling.

I decided to investigate. The toilet area is all sealed up so its difficult to see whats goin on as the access area is very small.

I noticed two things:
1) the joint attaching the pipe to the tank was drippin- not very much
2) there was a long damp area close to the back of the the toilet.

I called a plumber who first said it was condensation but then agreed with me that there was a leak. I had noticed for some time that there was running water in the bowl. The overflow has been now been adjusted but the pipe is still leaking at the joint. The joint was actually replaced and the guy placed some tape inside before tightened to secure it further. Im not sure why it continuing to drip.

In respect of the damp nothing was done. The guy checked the area around the waste pipe but found no leak. I have again called the same plumber & left a message because i am worried about the damp floor & also the leaking tank hasn't resolved.

He had suggested filling the area around the waste pipe with silocone form but is this wise when there is no evidence of a leak??

It is clear to me that a dripping pipe which is not near the damp area has not caused the marks on the ceiling below. I dont believe its condensation. I feel that because i am a girl its making it difficult to convince him that theres a problem.

I wondering if anyone can help me understand what the problem could be so i can make suggestions the plumber to convince him it needs fixing. I think the main reason for him not to act on it is access. He had to use a mirror to see what was going on & it a narrow space.

Please help me if you can. I feel really lost & dont know what to do.