From what i know recertified means, it has been tested and the smart counter has been reset. I'd contact customer support directly regarding further questions, especially if the warranty is in order. In my opinion this should be clearly declared and even be under a different article number, not shared or mixed.
In this case, we will refer you to our Galaxus Assistant, which provides direct contact options so that you can be helped accordingly.
https://www.galaxus.ch/help
In principle, the hard drive can be installed in the PlayStation 2, as it has a 3.5-inch form factor and a SATA interface that are suitable for installation in the PS2. However, the installation is complex and is only officially supported for certain PS2 models (v12 and v13), not for newer versions. In addition, the 3.5-inch size fits mechanically well into the PS2's hard drive bay.
The hard drive with SATA III connection, 2.5-inch design and 5400 rpm is basically compatible with the PS3 Fat, as it also supports 2.5-inch SATA hard drives. There is no official indication that the ST1000LM048 model is explicitly incompatible. However, there is no official confirmation from Sony or Seagate regarding compatibility with the PS3 Fat - the information is based on the technical specifications and current experience.
To install a 3.5" hard disk in your HP PC, you generally need to use a hard disk support or cage. These brackets are often built into the PC case and are used to secure the hard drive in place. Make sure that your PC has a bracket suitable for 3.5" hard drives. If it doesn't, you may need an adapter or an additional bracket.
As long as you have a free SATA III port, a free HDD slot and the relevant cables (power cable from the power supply unit and SATA cable), this is not a problem.
The photos showing the disc with the tone arm (without cover) are for illustration purposes only. Hard drives are always protected. They would be too vulnerable without it. There is no specific variant to look for, the drive will always be "closed".
That should fit. The computer is not that old and nothing has really changed with SATA since then.
A SATA hard disk only needs two connections. The narrow one for data and the wide one for power (page 23).
https://static.digitecgalaxus.ch/Files/2/8/3/5/3/2/4/4/100805918l.pdf
The socket with 4 pins is not needed.
In terms of physical size, for sure. According to various forums, the PS3 stops at 1TB, but I can't confirm that. With my PS4, things look different again. When converting, just make sure to first make a backup on an external HDD if you don't want to reinstall and adjust everything. (Google and YouTube help here).
However, if finances allow it, I would recommend an SSD (e.g. Samsung 860 Pro).