Typically if the deadline is Jan 15th then schools mean before midnight on the 15th. Given that there are applications coming in from international students in various time zones all over the world, you should consider it as midnight at the receiving school’s time zone. But seriously, don’t leave it so late that you are debating time zones.
Here’s a previous topic on time zone stamps for Gateway:
School tend to be more flexible with deadlines for some items such as teacher recommendations and transcripts which are generally out of the control of the student. If you have items like this which will be delayed, it is best to communicate directly to the AO at your chosen schools to let them know. I would not recommend submitting essays or parent statements after the J15 deadline since this reflects poorly on the ability to manage workload and deadlines, which is a huge factor in thriving at BS.
It sounds like there is some flux in the deadline this year due to Gateway not being available so there may be some extension of when materials are due. Note that admission offices are likely to be inundated on Monday morning with panicked parents and students having a freak out because of the technical Gateway snafu.