Non-generation of E-way Bill.

There will be no consequences
yes you can avail ITC

Yes you can avail ITC. For availing ITC, you need to satisfy the FOUR CONDITIONS as laid down under Section 16(2) of the CGST Act 2017 i.e. :

1). Possession of a Tax Invoice.
2). Received the Goods or Services.
3). Supplier must have deposited the tax.
4). Recipient must have filed the Return.

If the above 4 conditions are satisfied then you can avail ITC.

Generation of E-Way Bill is not the determining factor for claiming ITC under GST Law. Electronic Way Bill ( E-Way Bill ) is required only to track the movement of goods. Max to Max Penalty may be levied in the future for not complying with the provisions of the GST Law.

Yes, you can claim ITC, it doesn't matter whether e- way bill generated or not..