Can a 25U be put into a 25W 1SG position?

MOS mismatch at the 1SG level is discouraged but not prohibited. In the case you mention both are in the same career field 25 so not as big a deal as if someone from say 12 series was being considered for a 25 series slot.
I personally have slotted folks for 1SG positions as MOS mismatches within the same career fields for deployments where no Inbounds were projected. Also have slotted folks as career field mismatches for the same reason.
As a PVT the unit I served in had an Infantryman serving as our 1SG in an Engineer unit, no issues other than not asking him to show me how to lay block or do concrete. All the other First Sergeant stuff was fine. Unless it's changed the AR was 600-20 and 600-200.

While it's preferred to match the MOS sometimes a mismatch can't be helped. I've been slotted against an 11B 1SG position for the past 8 months as a 25W.

1SG(P) (Join to see) Yes its can and does happen and IS supported by regulation. Though not supposed to be the better plan, nor done commonly. And there are restrictions and requirements to assign a 1SG position outside ones PMOS.

See AR 614-200
"When possible, the 1SG will possess the PMOS of the authorized duty position, particularly in TOE company–level organizations. Soldiers will only be assigned outside their PMOS or CMF as an exception and with prior approval from HRC. These Soldiers must possess SQI “M” and be the only qualified Soldiers available to fill the vacancy"

Not usually. E-8 and -9 positions need to match the MOS, with exception for substitution MOS like 11C for 11B.

Good Question, so is it okay and is it possible to put a 25B402S in a 25W502S?

1SG(P) (Join to see) Yes. I am living proof. I spent 2 years as 1SG of a signal company which was a 25W slot and I am a 25U. I was also in a 11B5M slot as an HHC 1SG with the infantry and in a 92A5M slot in an HHC Sustainment company.

You can be put into any position as a 1SG.
As a 25U I was slated in a 11Z position at JRTC, as well as replaced an MP holding a 25U signal company position in a Sustainment unit. It all depends on who the CSM feels is best for the slot.

you need to look at the career progression Reg

As for your first 1SG position I would not recommend. I have personally have served in a 1SG position outside of my MOS but not until I was slotted as a HHC Bde 1sg. I'm a 13Z and I'm currently serving in 92A5M position which is a HHC for a sustainment BDE. I'm not sure this helped me get selected for USASMA but it did not hurt. Most will tell you a 1SG job is 1SG job which is true. Good luck in career.

Yep. Been doing it for the past 21 months.

How that iv gotten a few to respond. What going on is. I sent in a packet to transfer from the National Guard to a Army Reserve unit for my last 2yrs. They stop the packet till after AT. (27th May 2017) and don't wont me to leave. I been getting offers and offers E8 spots and now this 1SG job. We have a strength issue and I believe that's what is running this push to get me a good job to stay. Wanted to share this additional information.

Depends. Many units used to have Senior NCOs that could take the 1SG place. This was just a temporary replacement until he came back. Also if there Isa shortage of E8s then again a temp can be put in. Usually only a promotable SFC could actually replace a 1SG