That is the mounting point for night vision goggles. The following image shows a helmet with NVG mounted.
Helmet mounted NVG; image from lemt.by
The USAF has helmets with different mounting and some of the modern pilot helmets (like BAE Striker II, for example) have an integrated night vision device.
I believe it is exactly what your instructor has said - it helps when regaining control of the aircraft during a spin.
The correct procedure for recovering from such a maneuver is to apply rudder in the opposite direction. Then, keeping the control column centered, move it forward (for an upright spin) or backward (for an inverted spin).
The problem is, ...
The Su-27 and Mig-29 were the result of high-low concept subscribed by both the USAF and Soviet Air Force (VVS) in the 1970s. Basically, this involved the development of two different fighters, a high performance medium weight fighter crammed with every advanced technology (which made it expensive) and a low cost light weight fighter to make up the numbers.
It's the sensor of the IRST (InfraRed Search and Track) system.
An IRST allow an aircraft to search and track aerial or ground targets using passive infra-red radiation only thus reducing the probability of being discovered (for example using a Radar Warning Receiver).
The Su-27 can use it's IRST to track a target at very long distance and engage it using ...
The long thing has RWR (Radar warning Reciever) on its sides and has a drogue parachute in the middle. This image shows the rear part open after deployment.
Image from airplane-pictures.net
Incidentally, the aircraft serial number is 901, while the one in your image has a number 902.
I believe that these are static discharge wicks. You can see similarly sized/shaped wicks on a 1/32 scale models of the SU-27, as discussed here, but, more importantly, you can find them labeled with number 53 on the cutaway drawing below. The label is written as Разрядники статического злектричества, which, according to Google Translate, is "ESD arrestor" ...
If you are speaking of the grey volume, according to this cutaway by Alexey Mikheyev, it contains a Radar Warning Receiver/Electronic Intelligence System. Basically a system designed to detect if an hostile weapon system is locking/has locked on you.
As @RalphJ notes, it is not required. It is a design choice based on various considerations. The 'cone' in the Su-35 houses the RWR and the drogue chute. In case of F-15, however, the drogue chute is not used and the RWR antennae are located elsewhere (in the wing and vertical tail tips, to be exact).
The image below from a BAE systems document shows the ...
In a fighter you generally want to optimize fuel and ordinance capacity as well as have competitive performance. This use case generally leads to a design that is different than your average transport category aircraft. The SU-27 has some similar characteristics to the F-14 Tomcat and it should be noted
The aircraft had a large wing, clipped, with two ...
There can be many reasons for such a choice. The first is a single seat air-defense fighter, the other is a two-seat multirole air-superiority fighter according to Wikipedia. The cost can be another reason; depending on configuration it seems that the two aircraft have an overlap with both types starting around USD \$40 million per aircraft.
The Su-27 was design to fly escort for long distance bombers, whereas, the Mig-29 was designed for front line action. This distinction in the primary mission of the two aircrafts becomes apparent when you look e.g. at the range.
More fuel means more weight, means more powerful engines, means more fuel, etc.
Those are also mounts for Helmet Mounted Sight for the Vympel R-73 missile. Both the MiG-29 and Su-27 were equipped with this missile system.
I think F-35 pilots have this technology now but with a fancier helmet. The old ones on the MIGs looks like monocle.
The Su-30 is an modifications of the SU-27UB
The Su-35 is an Su-27 shaped aircraft with many new parts from the Su-34 (T-10BM)
Radar N035 Irbis-E PESA
Rear-looking self-defense radar
new fly-by-wire flight-control system
new fully-glass cockpit
Electronic-warfare self-defense system L175M Khibiny-M
Engine AL-37FU/ 117S
larger Air Intakes, no ...