Billboard at Uhud Gravesite and Women Forbidden Contradiction

Salam aleykum,
I have a question on a hadith I saw at the site of Uhud and I was wondering if anyone can explain it to me.

At the gravesite of Uhud there is a big and blue billboard (you can't miss it) with a hadith from at-Tirmidhi which says:

"The Messenger of Allah s.a.w.s. cursed women who visit graves."

Apart from the discussion we can have on why this big billboard is there and what negative thoughts it evokes about Saudia-Arabia and the treatment of women there in general etc., I was wondering if any knows the authenticity of this hadith. This is one issue.

Secondly (much more important), I read the following passage in a book I bought in Makkah: "It is recommended for women (..), to visit the graves as it was authentically reported that 'Aa'ishah (r.a.) asked the Messenger of Allah (s.a.w.s.) what she should say if she visited the graves, and he taught her what to say, without saying that it is not permissible for women to visit graves." We can read this by the way in many other books.

Now what to think of the previous hadith in light of the hadith that was lastly mentioned? I assume reconciliation is possible. How should I understand that big blue (and bold) billboard? If the Prophet s.a.w.s. cursed women who visit graves why would he teach 'Aa'ishah what to say in the first place?

Please your help here insha'Allah. Barakallahu fik.

First of all I would like to say ما شاء الله عليك Brother Harun. For someone who came to Islam a few years ago to be so diligent and insightful in your Islamic studies is extremely admirable and I too was pleased to meet with you in Belgium a few months ago. I pray that Allah increases your zeal to study. I am also happy to see that you have started to think critically about the hadith and are developing the mindset of a muhadith or faqih.

Now, let me look at the questions you are asking:

The authenticity of the Hadith

For the rest of the answer