Jabali

Anything from QNAP or Synology will do the job, personally I prefer QNAP.

Thanks LeadEater. 
I checked out both and it looks like Synology has sales and service offices in India. So we will probably go for that.

You will have to break the "Warranty Void if Removed" Sticker to open up the laptop to switch the SSD.
Honestly, I would just do it myself. If you have a little experience in Hardware it will be no problem. Bringing it to Acer would be a waste of money (in my Opinion)

I'm assuming you mean MS SQL and not a different SQL database engine like MySQL or Postgre?
 
Just give it more space?
 
MS SQL can use basically as many cores as you can throw at it, the limiting factor is data/table structure and query design. MS SQL is about as top class as you can get relational database engine wise.
 
Other factors to look at is the server setting of Max Parallelism so a single query can't take/block all CPU cores and degrade other running query performance.
 
What is the current specs of the server the database is on now? For a 50GB database you won't need 64GB of ram, unless it's some kind of special highly accessed database with odd access patterns 16GB will be fine and 32GB will be a lot.
 
Also why so much storage when the database is so small? For the most part data comes out of ram so putting blistering fast storage behind MS SQL won't necessarily lead to higher performance than another lower class but fast storage.

We have customers running SAP Business One environments with much larger SQL databases on servers with a single 6 or 8-core CPU, SAS 15K storage and 32-64GB of RAM without any performance issues whatsoever, so I agree with @leadeater here that there's really no point in throwing so much hardware at a rather small database.