I have three questions:
(1) Theoretically, a non-celibate layperson can, at any time of the day, seclude himself from sensuality, and practice satipatthana or anapanasati?
(2) Can a non-celibate layperson practice satipatthana or anapanasati on Uposatha?
(3) Concerning non-celibate laypeople, when the text says that they were rid of hindrances prior to stream-entry, does this mean they went celibate for some time?
Perhaps this question is best answered with another question! 
“Why did the Buddha lay down the Rule of Celibacy for Monks and Nuns but not lay people?”
Stream enterers and once returners are described in the Sutta’s as “still enjoying sensual pleasures”. The most frequently recommended meditations by the Buddha for lay people are the six recollections and metta, but there are some places were lay people are described who practice satipatthana from time to time (if I remember correctly). Having said that, anapanasati and jhana are often mentioned in relation to jhana, and in jhana you have transcended sensuality.
I think you can advance by following the Buddha’s recommendations for lay people: practice generosity, practice five precepts all the time, 8 precepts on Uposatha, practice bhavana, like the meditation topics mentioned above. And keep studying the Sutta’s.
Let’s think of two scenarios.
AN 7.50:
“But what, Worthy Gotama, is a break, taint, stain, or mar in chastity?”
[…]
However, they live the chaste life wishing to be reborn in one of the orders of gods. They think: ‘By this precept or observance or fervent austerity or spiritual practice, may I become one of the gods!’
They enjoy it and like it and find it rewarding.
This is a break, taint, stain, or mar in chastity.
This is called one who lives the chaste life impurely, yoked by the yoke of sex. They’re not free from rebirth, old age, death, sorrow, lamentation, pain, sadness, and distress. They’re not free from suffering, I say.
Now, a second scenario:
It’s all about intention. And one cannot hide the intention from themselves. One cannot trick themselves into the “right” intention, while holding the wrong intention secretly from themselves.
So, yes, a lay person can at any time of the day seclude themselves from sensuality, although realitiscally, even with a honest intention, it will take a lot of time for it to sink in. A wild citta cannot be ordered what to do only based on intention.
Now, a lay person practicing correctly needs to see sensuality as a danger, and consequently, not practicing the eight precepts as a concession to the wild citta that as soon as possible needs to be addressed, and not something just ok to do without any consequences in your life, and in your practice.
The Buddha gave apropriate training for lay people, like the five recollections. Thinking about your death and the death of your loved ones correcly, for example, will surely make any lay person advance.
Do you have a reference for the Sutta you quoted?
Sorry, I edited my reply and included the reference.
No it doesn’t. Unfortunately while celibacy is relatively easy condition to fulfill, wisdom and understanding is much more demanding condition for substantial progress in Dhamma.
If you are interested about your relationship with Dhamma, here is certain standard:
(1) This Dhamma is for one with few desires, not for one with strong desires.
(2) This Dhamma is for one who is content, not for one who is discontent.
(3) This Dhamma is for one who resorts to solitude, not for one who delights in company.
(4) This Dhamma is for one who is energetic, not for one who is lazy.
(5) This Dhamma is for one with mindfulness established, not for one who is muddle-minded.
(6) This Dhamma is for one who is concentrated, not for one who is unconcentrated.
(7) This Dhamma is for one who is wise, not for one who is unwise.
(8) This Dhamma is for one who delights in non-diversification, who takes delight in non-diversification, not for one who delights in diversification, who takes delight in diversification.
AN 8:30
If you feel inclination towards such standard like below, you can make a progress in Dhamma:
“Gotami, those things of which you know: ‘These things lead to passion, not to dispassion; to attachment, not to detachment; to amassing, not to dispersal; to ambition, not to modesty; to discontent, not to content; to association, not to seclusion; to idleness, not to energy; to luxury, not to frugality,’ of them you can quite certainly decide: ‘This is not the Dhamma, this is not the Discipline, this is not the Master’s teaching.’ But those things of which you know: ‘These things lead to dispassion, not to passion; to detachment, not to attachment; to dispersal, not to amassing; to modesty, not to ambition; to content, not to discontent; to seclusion, not to association; to energy, not to idleness; to frugality, not to luxury,’ of them you can quite certainly decide: ‘This is the Dhamma, this is the Discipline, this is the Master’s teaching.’ ”
Vin. Cv. 10:5; A. 8:53
