1. Definition and formal requirements of written legal statements or legal statements legally binding if the law requires written form
England and Wales: Where there is a statutory requirement for a contract to be entered into in writing, it will be a matter of statutory interpretation as to what "writing" means in that context.
Scotland: Section 1(2) of the Requirements of Writing (Scotland) Act 1995 specifies certain documents which must be made in writing.
2. Examples for legal statements and contracts where written form is required
England and Wales: Guarantees (s4 of the Statute of Frauds); Assignment of Copyright (ss90(3) and 222(3) of the Copyright Designs and Patents Act 1988.
Scotland: A contract or unilateral obligation for the creation, transfer, variation or extinction of a real right in land (s1(2)(a)(i) of ROWSA; Assignment of registered trade mark (s24(3) Trade Marks Act 1994).
3. Are there special legal provisions for digital archiving and storage of electronic documents? If yes, please describe them
4. Main and relevant court practices
England: English case law generally indicates that electronic documents will satisfy a statutory requirement for writing, for example in J Pereira Fernandes SA v Mehta  EWHC 813 the High Court held that an email containing the essential terms of an offer of a personal guarantee (which had been accepted orally and unconditionally by the other party) could constitute a sufficient note or memorandum of the agreement for the purposes of the Statute of Frauds.
5. In which cases are documents with wet ink signatures required?
In certain circumstances a wet ink signature will be required for registration purposes, for example real estate documents that require to be registered in the Land Registry (England & Wales) or Land Register (Scotland).
6. List of the relevant national legislation
EU Regulation No.910/2014 on electronic identification and trust services for electronic transactions in the internal market (eIDAS), Electronic Communications Act 2000, Interpretation Act 1978 (England & Wales), ROWSA (Scotland), The Electronic Documents (Scotland) Regulations 2014 (Scotland).
7. Are the following use cases deemed as written legal statements / legal statements legally binding if the law requires written form in your jurisdiction?
1. Electronic document signed with qualified electronic signature (QES as defined in the eIDAS Regulation) and with a time stamp
2. Electronic document signed with qualified electronic signature (QES as defined in the eIDAS Regulation) without a time stamp
3. Electronic document signed with advanced electronic signature (AdES as defined in the eIDAS Regulation) and with a time stamp
4. Electronic document signed with advanced electronic signature (AdES as defined in the eIDAS Regulation) without a time stamp
5. Electronic document signed with advanced biometric signature
6. Electronic document signed with a simple, standard electronic signature (SES)
7. Scanned electronic version of the original paper-based document with handwritten signature sent as an attachment in ordinary e-mail without an electronic signature, but with standard e-mail signature panel
8. Legal statement sent as a text of an ordinary e-mail without an electronic signature, but with a standard e-mail signature panel
9. Legal statement sent in an SMS
10. Electronic document with a copy-pasted image of a handwritten signature, sent as an attachment of an ordinary e-mail
11. Electronic document with the typed name of the signer and sent as an e-mail attachment
12. Electronic legal statement sent in a social-media message sending application (e.g. Messenger, Viber, LinkedIn, Facebook message, etc.)
13. Electronic legal statement sent in a chat application
14. Electronic document created on an electronic platform ensured by the other party requesting the legal statement (without an electronic signature) by another party whom the operator of the platform granted access
15. Electronic document signed in DocuSign/Adobe Sign with a simple standard electronic signature (no QES or AdES)
16. Electronic document signed with a qualified electronic seal as defined in the eIDAS Regulation
17. Agreements accepted by the other party online, by ticking a checkbox or by clicking on a button ("click on agreements")
7.1 Remarks/Comments to use cases (if yes/no answer is not sufficient)
The above answers are subject to the following overriding comments. Electronic signatures will be capable to execute documents (including in England and Wales, a deed) provided that (a) the person signing the document intends to authenticate the document; and (b) any formalities relating to the execution of the document are satisfied. As noted above, there are circumstances where an electronic signature will not be permitted due to statutory requirements such as the registration of real property documents. It is also important to emphasise that use of the examples above will have different evidential weight, and in Scotland an electronic signature will only have probative (self-proving) status if an AdES is used.