1)What is your understanding of Blockchain?

Blockchain is a technology which is a combination of distributed database systems and cryptography which was already in existence.
Blockchain usually contains "n"number of block by forming a chain of it.
Block is the one which contains certain things like:
1: Block number.
2: complete data or record.
3: previous hash key.
4: mining key.
Thus Blockchain is used to store the data and records for permanently without any tamper to the data present in it.

2)What is the core problem blockchain trying to solve?

The main core problem is that international backing security crisis which occurred in 2008. And other three major cause is :

1) Authentication
2) Security
3) Third party Trust

3)What are the features that the blockchain will give you?

1: Verifiable
2: Immutable
3: Tamper-proof
4: Unchangeable
5: Decentralisation

4)What are all the things the block contains?

Block is the one which contains certain things like:
1: Block number.
2: complete data or record.
3: previous hash key.
4: mining key.

5)How is the verifiability of blockchain can be achieved?

Verifiability is achieved by making a track over the hashing key present when the block contain is hased.
Thus in Blockchain each block contains the previous black hash key and the data , when we hash the current block it will result in new or current hash key of the block. Thus by making a track of this current hash key when can able to verify the block even when a error or modify occur to a person in an organisation.
Note : each block contain an unique hash key , thus even a small change in the block data will result in new hash key.
By using this hash key verifiability is achieved.