Does collecting saliva and swallowing it break the fast?
Swallowing collected saliva does not break the fast, but it is an unnecessary and meaningless act.
Someone wiped over his shoes after wearing them in a state of purity, then took them off and prayed without them?
Ablution is not invalidated by taking off leather socks or shoes after wiping over them. However, whoever takes them off after wiping must wash his feet only. If he prayed without washing his feet, he must wash his feet and repeat the prayer. And Allah the Almighty knows best.
What is the ruling on the follower`s prayer if the Imam stands for a fifth rak`ah?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If the Imam stands up for an extra unit (rak‘ah) of prayer out of forgetfulness, he must return to the sitting position as soon as he remembers, and he should perform the prostration of forgetfulness (Sujud al-Sahw). It is the duty of the congregants (Ma’mumin) behind him to remind him. However, if the Imam is in a state of doubt regarding the extra unit (and not certainty), it is not permissible for him to return.
As for the congregants: anyone who is certain that the Imam has stood for an extra unit is forbidden from following him. In this case, the follower has two choices: either intend to separate from the Imam (Mufaraqah) and finish the prayer alone, or wait for the Imam in the sitting position and perform the final salams with him—the latter being the preferred option. If a follower knowingly follows the Imam into an extra unit, their prayer becomes invalid. However, if a follower is in doubt and not certain of the mistake, they must continue following the Imam, as the Imam was appointed to be followed.
It is stated in Al-Majmu’ (Vol.4/P.145): 'If [the Imam] stands for a fifth rak‘ah, the follower should not follow him, even if it is assumed that the Imam might have omitted a pillar from a previous unit; because if the reality is known, following him is impermissible since the follower has certainly completed their own prayer. Even if the follower had missed a previous unit (Masbuq) or was in doubt about performing a pillar like the Fatihah, and the Imam stood for the fifth, it is not permissible for the latecomer to follow him in it. This is because we know that this unit is not counted for the Imam and that he is mistaken in performing it.' And Allah the Exalted knows best.
What is the ruling on the Friday bath (ghusl al-Jumu'ah)?
The Friday bath is a confirmed Sunnah, based on the Prophet's (peace be upon him) saying: "Whoever performs ablution on Friday, it is good for him, and whoever takes a bath, bathing is better." (Reported by Abu Dawud and al-Tirmidhi who said it is a hasan hadith). It is recommended for everyone who wants to attend the Friday prayer, even if they are not from its usual attendees, like a woman or a boy.
If a person is in a state of major impurity (junub) and intends by his bath both lifting the major impurity and the Friday bath, he achieves both. If he intends only one of them, he achieves only what he intended. And Allah the Almighty knows best.