Is there a disorder similar to dyscalculia but only for time/date arithmetic? (also memory) Something that might be used to describe an individual who:


can perform arithmetic at an advanced level (e.g. post graduate)
does not generally struggle with memory
can easily remember the relative ordering of past events
is young/not at an advanced age
struggles to perform basic calculations when the numbers represent units of time (e.g. "it is 6pm, what time will it be 5 hours from now?")
has difficulty reading an analogue clock
has difficulty remembering the year/date an event occurred
has difficulty remembering the current date/their age
Dyscalculia includes or at least is closely related to difficulty reading an analog clock, says Wikipedia citing a PhD thesis which I haven't checked myself. Also, without a citation this time, Wikipedia adds "Difficulty with time, directions, recalling schedules, sequences of events. Difficulty keeping track of time. Frequently late or early." General comorbidity with ADHD is also mentioned.

There are obscure forms of marginal dyslexia (there was a question here recently), so I don't doubt there are probably obscure/marginal forms of dyscalculia that may or may not have received much attention separately. Research into the heterogeneity of dyscalculia is a fairly recent endeavor. Quoting from a recent paper on the topic


  time processing [is] more often affected by number processing than vice versa. (e.g., Cappelletti et al., 2011) Also space and time have demonstrated to exert reciprocal influence on each other. 


So what you describe (time but not general number dyscalculia) is probably fairly rare. The more focused article of interest by Cappelletti et al. looks only at acquired cases, following brain lesions; however if my analogy with marginal forms of dyslexia holds, my crystal ball says eventually the developmental version will be found and studied.

As for the final part of your list of symptoms, I don't know how researched the relationship between remembering times and manipulating them is, but it seems obvious that the former can affect the latter.

References (spelled out):


Ulf Träff et al., Heterogeneity of Developmental Dyscalculia: Cases with Different Deficit Profiles, Front Psychol. 2016; 7: 2000. doi:  10.3389/fpsyg.2016.02000
Cappelletti M., Freeman E. D., Cipolotti L. (2011). Numbers and time doubly dissociate. Neuropsychologia 49, 3078–3092. doi: 10.1016/j.neuropsychologia.2011.07.014