Can I use the Rival crankset with a Shimano 11-speed rear derailleur?

Partially - Shimano and SRAM 11-speed chains are cross-compatible in width. However, SRAM shifters and Shimano derailleurs are generally not cross-compatible without a cable pull adapter.

What is the 53-36T gearing equivalent in road cycling terms?

53-36T is a semi-compact combination. The 53T outer ring is standard for road racing; the 36T inner is between a standard 39T and compact 34T, giving a good mid-range option for flat to moderately hilly roads.

Does this work with a Shimano 11-speed bottom bracket?

No - the GXP spindle requires a SRAM/Truvativ GXP bottom bracket. Shimano bottom brackets use a different spindle interface.

SRAM

Sram CrankSet Rival 172.5MM 11 Speed

Name: Sram CrankSet Rival 172.5MM 11 Speed
Brand: SRAM
SKU: CMB_LONGSHINE_00.6118.249.007
Price: 18750.00 INR
Availability: InStock
Author: InstaSport Editorial

₹18750.00

Description

Specifications: Color:Black Spindle Interface Type:Truvativ GXP Pedal Spindle:9/16" Chainring BCD:110 Rings:52/36 BB Included:No Crank Intended Use:Road Defined Color:Black Spindle Diameter:24-22 Stepped Chainrings Included:Yes Crank Length (mm):172.5 Drivetrain Speeds:11 Number of Chainrings:Double