I just bought a Nikon D3300 from a guy from eBay. (Actually not eBay, but a Dutch website, same concept). It came with 3 lenses: an 18-55mm kit lens, a Tamron 18-270mm f/3.5-6.3, and a 50mm f/1.8 lens, all containing autofocus motors. As soon as I reach past 50mm in the zoom range, the camera stops autofocusing completely. It works perfectly fine as soon as I zoom out under 50mm. This is the same on both the kit lens and Tamron superzoom lens. They still try to focus since I hear a clicky sound which you always hear when auto focussing, but it won't move the focus ring. Anybody knows what's wrong with it?
It sounds like someone has been moving the focusing ring on lenses with geared autofocus (AF) motors when AF is turned on. This can damage the autofocus mechanisms of certain types of autofocus lenses. It depends on which type of AF motor technology the lens in question uses.
Geared AF Motors
Lenses with geared AF motors must be switched to manual focus (MF) using the AF/MF switch to be manually focused without risking damage to the AF system of such lenses. This is because there is a hard mechanical connection between the AF motor and the focusing ring. Most such lenses will rotate the focusing ring when AF is moving the focusing elements. You should never attempt to manually focus such lenses when AF is turned on!
If your 18-55mm kit lens was the one included with the D3300 in a kit when it was new, it could be either the AF-S 18-55mm VR II included with earlier D3300 cameras or the newer AF-P type (see below) included with later D3300 cameras in some countries or in "gray market" kits. If the person who sold you the D3300 included an older AF-S 18-55mm kit lens and kept the newer 18-55mm AF-P lens, your lens is one with a geared AF motor.
If your Tamron 18-270mm lens is the 'PZD' version, it has a geared mechanism connecting the AF motor to the focusing elements.
Lenses such as the AF-S Nikkor 50mm 1:1.8 G use a type of motor to move the focus elements known as a Silent Wave Motor (SWM). The technology was first developed by Canon, who refers to it as an UltraSonic Motor (USM). It has since been adopted by many lensmakers and is known by such monikers as Supersonic Wave Drive (SWD) - Olympus, Supersonic Drive Motor (SDM) - Pentax, Supersonic Motor (SSM) - Pentax, Hyper-Sonic Motor (HSM) - Sigma, and Ultrasonic Silent Drive (USD) - Tamron.
The design uses rings vibrating at very high frequencies to produce the torque needed to move the lens' focus elements. Because these rings are not directly geared to each other, when the focus ring on an SWM lens is turned it allows them to slip in relation to each other without risk of damage to the focus motor. Most such lenses will not move the focusing ring when the AF motor is moving the focusing elements. It is also quite normal with this type of lens to be able to continue to move the focus ring indefinitely even after the focus elements in the lens have reached the end of their travel at either infinity or the lens' minimum focus distance.
Stepping/Linear Motor AF
A newer type of AF motor is called 'stepping motor AF'. Canon introduced their version, the 'STM', in 2012. Nikon's first F mount lens with a stepper motor, designated AF-P, was introduced in 2016. Pentax calls their stepper lenses PLM.
Another approach very similar to the stepper motor is the linear electromagnetic (LEM) AF motor used by Sony and Panasonic.
In most such lenses, the focusing elements are always moved by electrical signals to the AF motor. Even moving the focusing ring to manually focus the lens turns a switch that sends an electrical command, via the camera body, to the AF motor to actually move the focusing elements of the lens. These are sometimes referred to as 'focus-by-wire' AF systems. Nikon calls their lenses with stepper motors 'AF-P' lenses. Only Nikon DSLRs made since about 2013 work at all with AF-P lenses. AF-P lenses can not even be manually focused when mounted on older Nikon bodies.