I. What is prohibited?
We know that on י"ז בתמוז you are allowed to wear leather shoes, wash etc. and the fast only starts in the morning. Why is that?
The Gemara in Rosh Hashana 18b, brings a pasuk in זכריה that lists 4 fast days. The Gemara to resolve a contradiction in the pasuk states the following rule:
When there is peace (according to most Rishonim the Beis Hamikdash standing) the 4 days are holidays. When there is a גזירת המלכות all 4 fast days are מדברי קבלה and therefore all 4 are like ט' באב, e.g. the fast starts at night and all the 5 עינויים are נוהג. When there is neither a גזירת המלכות nor a Beis Hamikdash then it is רצו מתענין רצו אין מתענין, in other words it is voluntary. The gemara then says that ט' באב is different because הוכפלו צרות (there is a machlokes rishonim what this means, does this mean that ט' באב is even today מדברי קבלה, or is ט' באב now also not but we were מקבל to fast with the 5 עינויים anyway) and on ט' באב all the 5 עינויים apply and the fast starts at night.
The Rishonim comment on this that בני ישראל were מקבל these 3 fast days as a חובה (like with maariv) and therefore nowadays you have to fast. However, the קבלה was only partial, it was only to fast during the day and did not include the 5 עינויים.
II. When were the walls of Yerushalayim breached?
Everyone agrees that the walls of Yerushalayim were breached on י"ז בתמוז in the time of the Romans (בית שני). However, there seems to be a machlokes the בבלי and the ירושלמי regarding the בית ראשון. The pasuk in ירמיה says explicitly that the wall was breached on ט' תמוז and this is the way the בבלי assumes. However the ירושלמי makes a startling statement that what is written in the נביא is wrong and the wall was really breached on the 17th. Tosafos in Rosh Hashana states that the נביא knew the correct date but since the people were mistaken as to the date the נביא recorded the incorrect date.
The Minchas Chinuch is bothered by a number of questions.
1. How can there be a machlokes R' Akiva and R' Shimon about what day in Teves was observed (the tenth or the 5th)? Why didn't they just see what people did?
2. According to the Bavli the walls of Yerushalayim in the first Beis Hamikdash were breached on the 9th of Tamuz. If so, why do we fast on the 17th? After all, the pasuk in Navi is clearly talking about what happened during the first Beis Hamikdash and therefore the chiyuv mi divrei sofrim should be on the 9th.
He answers that the Navi never set a specific day for the fast only a month. That is why the pasuk only mentions months. After the churban bayis sheini, chazal decided to set specific days for the fasts.
III. What is the din when there is a gezera?
From the simple reading of the Gemara there is a chiyuv mi divrei kabala for all the 4 fasts and they are all full day fasts with the 5 עינויים. During the holocaust RYBS held that it was a time of gezera and therefore mi dina everyone was chayav to fast a full day. In fact, the שער הציון in סימן תק"נ seems to say this.
However, it is not so simple. The Rambam doesn't make a distinction between a שעת גזירה and other times. He simply writes that there is no chiyuv to fast a full day on the other fast days. The Aruch Hashulchan also writes that nowadays the other fast days are less severe then Tisha B'Av period. It sounds like once there was a period of no gezera the other 3 fast days were בטל and now even if there is a gezera we only fast because of the minhag.