The image caption is a little long, as it makes the text slightly too small for me to read easily. Maybe cut down on some of it?
Foundation webcrawlers are to monitor SCP-4686 and prevent civilian access to the website.
Technically, web crawler is two words, however I think I have seen it written as one word in a few SCPs. Also, as far as I know, the web crawler itself wouldn't be capable of preventing access to the website. That would be a job for a human or another automated system.
Civilians who have accessed SCP-4686 are to be amnesticed.
This is one of the more unique ways of naming the action of applying amnestics. I'm familiar with amnesticised, amnesticized and amnestized, however I may have just missed other SCPs that use this spelling. I do prefer those other ones though.
has three fields
I think you should specify that these are "input fields".
When a person (the "requestor") fills the first two fields accordingly and clicks the “Request Hug” button, an entity referred to as SCP-4686-1 will emerge and grow from the monitor of the "requestor’s" device and proceed to embrace said "requestor".
This sentence runs on a little too much, and uses 'and' three times. Maybe consider separating it into two sentences?
If left blank it will automatically be filled with “DEFAULT”
I actually think this can just be completely cut. In the table it's obvious what default means, so this sentence doesn't really add anything.
I'm not entirely sure that the "" around some words are needed. I'm less sure about some of the words, but I don't think they're needed around requestor.
closely resembling that of a rabbit or a dog, specifically, an Angora rabbit, or a Samoyed dog.
The commas after specifically and rabbit are not needed.
The website will then enter a refractory period lasting from 24 to 145 hours where it will be unavailable to take in requests.
Does this mean requests made in this time fail, or does it just not take them? If the former, nothing needs changing. If the latter, you need to add something about how some requests fail.
SCP-4686 will wave one of its limbs
Should be SCP-4686-1
Any attempt to apprehend the entity has failed as the entity is capable of becoming incorporeal.
Should be a comma after failed. Also, either replace the second use of 'the entity' with 'it', or replace the first use of it with 'SCP-4686-1'
The entity also affects any recording devices pointing at itself, within an unknown area around itself, distorting or corrupting any data within these devices.
You can probably remove the 'within an unknown area around itself' clause. Also, maybe change the final section a little, because at the moment it seems like it corrupts all footage on the device, not just footage of itself. Whether this was your intention or not, I much prefer it just affecting pictures and videos of itself.
Denied
This should probably be 'Failed'. If this was a conscious choice to use denied over failed for this request, I'm not a fan. It seems to be an attempt to add humour to an entirely non-humorous article.
Foundation latest attempt at shutting down the website. Website remained accessible but SCP-4686-1 was not able to manifest.
I prefer something like "The Foundation's latest attempt at shutting down SCP-4686. The website remained accessible but SCP-4686-1 was not able to manifest."
Website returned to its normal operations.
Again, I think I'd namedrop SCP-4686 in this.
SCP-4686’s refractory period has been observed to be reduced in half.
Replace this with either 'reduced by half', or 'reduced to half of its original length'.
has started to appear “thinner” than usual
Thinner probably doesn't need the quotation marks. Maybe replace it with slimmer? That's probably not necessary though.