Looks like you already decided but just sharing my experience so that others also know how to handle BSNL.
Is there any rule which says that a consumer must use the router provided for by BSNL?
No, there is no such rule.
Because the BSNL in my region insists that we need to take the one provided by them.
They are trying to be over smart. It is upto you to buy from them or from outside.
How good are the routers provided by them?
The wifi range is average and I get a speed of 50 mbps via wifi. Speed via LAN cable is good which is again 50 mbps up and down in my case. My modem never hangs and it connects super fast. I haven't faced any problem with it so far other than the okayish wifi range.
Anyone who has any experience with BSNL/MTNL please share them. Will apply for subscription tomorrow.
It depends from area to area. In my area, which is a small town, BSNL is good. I consistently get a speed of 50 mbps up and down. Downtime is minimal because fiber net gets down only if the wire is broken or there is something wrong from back end. The wire broke once in last year because of a large govt building construction. It took a few days to get resolved because of the local SDO who was trying to be over smart and saying that I was responsible for the security of wire coming to my house. They finally fixed the wire in just one day after I messaged their General Manager. Back end problems get resolved in one day max. There were about 8-10 down times in last one year and most get resolved in a few hours.
BSNL charges one month advance bill as security deposit (It is without tax) and 500 security deposit for modem. The modem security deposit may change so check bsnl website for more details. There are no other installation charges by bsnl. These days BSNL is trying to hand over the fiber installation and maintenance to local vendors so the vendor may demand some installation charge. I pay 1100 per month. My plan is 50 mbps till 600 GB, 2 mbps beyond. 849 + modem rent + tax = 1100. Below screenshot is via VPN.