Wa alaikum assalam
In my humble view from a Quranic perspective, a bridal due (ujur) would be a pre-requisite to establish the contract of marriage (4:24; 60:10).
With regards your second question, indeed, the classical sources carry very interesting, wide ranging discussions on whether the term 'nikaah' inherently / primarily signifies coitus.
[1] I personally feel that 'coitus' is somewhat implicit to complete 'nikaah' which seems to be supported by a couple of verses at least.
If we note, 2:235 where the Quran says
'wala ta'zimu uq'data l-nikah hatta ...' which I would loosely translate as
'And do not resolve on the tie / knot of marriage until ...', there is more than a suggestion that coitus would complete the marriage bond (nikaah). This is also then supported by the reduced responsibility of half the return of the dower (2:237) and no 'waiting period' (iddat) if the marriage was not consummated (33:49) and a divorce was pursued.
So
'coitus' seems to be an inherent part of the process of Nikaah. Therefore, I would posit the argument that albeit
'nikaah' does not mean coitus exclusively, it is a process which carries elements such as intention, a contract, and the intention to consummate which is a requirement to complete the bond. Hence, the interesting classical discussions on the matter.
I hope that helps, God willing
Joseph.
REFERENCES[1] Edward Lanes captures some of these ancient discourses on the matter which are worth perusing with counter perspectives.
http://www.studyquran.org/LaneLexicon/Volume8/00000102.pdf