Praise be to Allah.
Praise be to Allah Who has guided you, for you would not be guided if Allah had not guided you. Praise be to Allah Who has brought you back to the Straight Path of Truth. We ask Allah to make you one of those of whom He says (interpretation of the meaning):
"While as for those who accept guidance, He increases their guidance, and bestows on them their piety." [Muhammad 47:17]
With regard to your first question, we have already answered it on this website. Briefly, it is permissible for you to marry this woman if you both repent to Allaah. The child should be named after its mother, according to the consensus of the scholars.
In response to your second question, it is not permissible at all to offer prayers outside their proper time. Allaah says (interpretation of the meaning):
". . . Verily the prayer is enjoined on the believers at fixed times." [al-Nisaa’ 4:103]
"Then, there has succeeded them a people who have given up the prayer [i.e., have made their prayers to be lost, either by not offering them, or by not offering them perfectly, or by not offering them in their proper, fixed times, etc.] and have followed lusts. So they will be thrown in Hell." [Maryam 19:59]
"So woe to those performers of prayers who delay their prayer from their stated fixed times." [al-Maa‘oon 107:3-4]
It is not necessary to know whether the floor of the office or workplace is clean or not, because the basic rule is that any place is clean unless you come to know otherwise. The Prophet (Peace & Blessings of Allaah be upon Him) said: "The earth has been made for me a mosque and a means of purification. . ." So choose a suitable spot and pray there at the appropriate times. Beware of delaying your prayers, especially Salaat al-‘Asr (the mid-afternoon prayer), because the Prophet (Peace & Blessings of Allaah be upon Him) said: "Whoever misses al-‘asr, it is as if he lost his family and his wealth." (Agreed upon; this version was reported by Muslim, no. 992).
Refer to question # 333 for information on a similar matter.
I ask Allaah to help us all to repent sincerely and to adhere to His religion and understand it properly. May Allaah bless our Prophet Muhammad.