Meosos said:
How strong are Bolas mental powers and how are his instant death spells work ?
http://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=430751
There are many cards, aka spells that nicol bolas that allow for BFR/instant death.
Mostly in lines of 'destroy via black which kills regardless of status' or 'exile into another dimension'
Basically for mental powers, they allow for telepathy and controling 'turns' in other words a planeswalkers mind.
There is no resistance to this generally in the mtg verse minus a few spells.
http://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=430727
He can also counter 'magic spells'
http://gatherer.wizards.com/Pages/Search/Default.aspx?action=advanced&flavor=+[nicol]+[bolas]
It is generally speaking a good idea to use flavor text via cards to get the idea where his abilities come from.
Feat Wise:
Nicol Bolas defeated Jace, who specializes in mind manipulation and illusions.
He also defeated Lillianna who specializes in black magic, aka necromancy and death manipulation. He can also one shot most 'weak' planeswalkers.
Defeated all of the gatewatch, which together defeated a High 2-A being.
Killed Ugin premending who is a non corpeal spirit dragon.
Abilities:
Mind hax via making people 'forget their abilities' and illusions/
Void Manipulation and BFR via black and blue magic.
Time hax via jumping timelines
Mana/Energy Absorption via Shards of Alara arc, which he turned an entire plane as an energy factory basically (although partially unsuccesful due to story meddling)
These are the general ones, but again.
Taking a look at the cards affiliated with him as well as the planeswalker cards are good places to start and I can clarify.
TLDR: Discard/Exiling Cards = Mind Hax and Void Hax
Exile in battle = BFR
Extra Turns = Time Manipulation
https://magiccards.info/query?q=!Nicol+Bolas,+God-Pharaoh
His exiling is also pretty good, as it is permanant and you cant get out (i know sounds nlf unless you are resistant)
Most of the time these abilities are used to those comparable to his level, which emperor obviously compares (minus a few aspects)