No.
 

In my NS app, there is a button to activate Combined travel discount to get 40% with some conditions. - Can I activate this discount to get 40% off? Do I need any plan to get this 40% off or i can just use this button to activate 40%

You may only enable Combined travel discount if you are travelling together with someone who has a season ticket during the off-peak hours. Since neither you nor your partner has a season ticket, you cannot use that option. If you enable it without travelling together with someone with a season ticket, you don't have a valid ticket and can be fined.
 

Can me + my partner both activate 40% discount using button in App?

Not unless you are both travelling together with someone who has a season ticket.
 

What is the difference between Combined travel discount vs Weekend Voordeel ?

Weekend Voordeel is a season ticket that gives you, as season ticket holder, 40% discount during the weekends. Combined travel discount only applies if you are travelling together with a season ticket holder. If either you or your partner has a Weekend Voordeel season ticket, or any other season ticket, the other can use combined travel discount to get 40% discount without having to have a season ticket.

See this page for more information on combined travel discount.

@2. you could hence also use the discount IF you know someone with subscription and travel with her/him. It does not need to be your partner. The discount however is ONLY valid on off-peak hours!!

@4. Note that there is (weekend) Voordeel=discount and VRIJ=free. First is only 2€/month, the latter 32/month. But with this you can travel all around the whole of NL during all weekends in the month (and FR from 18.30 too). This is less as a return ticket over the longest possible distance and so a great way if you want to see some more of this flat country by the sea.

With all these FLEX subscriptions you can only change after use it at least 1 month. Its easy done via the mijnNS - myNS function, access via site of NS, not via app.

Wow.. This is the exact answer I was looking for. It is clear to me now. I really appreciate your help. You are genius. Thank you so much.