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Also in the 1842 Postal Directory for Glasgow, John LAURIE "bookseller, bookbinder, stationer and librarian" at 56 Main St Gorbals.

Another entry for  John LAURIE "bookseller, bookbinder, stationer and librarian" at 218 Argyll St. In 1842 Post Office Directory, there is a James C BROWN, bookseller and stationer at this address.

This article on familysearch is useful for describing marriage by license
https://www.familysearch.org/en/wiki/Marriage_Allegations,_Bonds_and_Licences_in_England_and_Wales

As I understand the legal age for marriage was 12 for girls and 14 for boys, though if underage they needed consent from parent or guardian.

1753 marriage act:
https://en.wikipedia.org/wiki/Clandestine_Marriages_Act_1753

Modified to add:
I have just read though that the minimum age for marriage changed in 1763 to 16 years, but I can't find a reference for this. Looks like it changed in 1929. 
https://www.parliament.uk/about/living-heritage/transformingsociety/private-lives/relationships/overview/lawofmarriage-/

In any case, yes, in 1770 a 17 year old could marry - with consent from parent/guardian.

Yes, you can obtain a UK (England and Wales) birth certificate for 1855, and both parents' names should be listed. If the child was illegitimate though there will usually only be the mother's name.

Some info here:
https://www.familyhistory.co.uk/births-marriages-and-deaths/

You can order through the GRO, digital birth certificates can be ordered for only £2.50
https://www.gro.gov.uk/gro/content/certificates/login.asp

Modified to add:
If you are after a birth certificate from Scotland, then you search and order through Scotlands People. You have to buy credits to use when ordering:
https://www.scotlandspeople.gov.uk/

Tivoli House shows on this 1907 map:
https://maps.nls.uk/geo/explore/side-by-side/#zoom=17.3&lat=53.36171&lon=-6.21041&layers=6&right=ESRIWorld

Modified to add:
Possibly this house on this 1837 map (bottom left most house).
https://maps.nls.uk/view/246835526#zoom=7&lat=7335&lon=1029&layers=BT

I see on the RHS of the 1837 map the "road" or area along the coast is called Raheny Strand.

For interest, 3 Palermo St Mentone seems to be Annie's brother's home. Her brother Edward Spencer MEREDITH, a jockey died in 1936 and family notices have this address. eg
https://trove.nla.gov.au/newspaper/article/11034193  (1st column, near the middle)

So possibly Peter Joseph and Annie Mignon did not stay together long. I can see her on the 1949 electoral roll at that address.