Discrete variables - Mean comparison and model

[Carla RAS]

Hi.
Within the explanatory variables of a multiple regression model I am working on, there are two variables:

1. Number of chronic illnesses - this variable was created from information on the number of illnesses a person reported for other questions (eg, do you have hypertension?, do you have asthma? If they answered "yes" to these two questions, 2 was added to the variable "number of chronic diseases" for that person, etc.)

 tab cd
   cd |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        807       33.05       33.05
          1 |        761       31.16       64.21
          2 |        505       20.68       84.89
          3 |        225        9.21       94.10
          4 |        106        4.34       98.44
          5 |         38        1.56      100.00
------------+-----------------------------------
      Total |      2,442      100.00

2. Number of medications. This variable was collected by asking the number of medications that he usually used (how many pills, creams, or other medications do you currently use?).

tab med

med |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        297       12.16       12.16
          1 |        366       14.99       27.15
          2 |        409       16.75       43.90
          3 |        399       16.34       60.24
          4 |        326       13.35       73.59
          5 |        213        8.72       82.31
          6 |        144        5.90       88.21
          7 |         94        3.85       92.06
          8 |         73        2.99       95.05
          9 |         57        2.33       97.38
         10 |         47        1.92       99.30
         11 |          9        0.37       99.67
         12 |          4        0.16       99.84
         13 |          2        0.08       99.92
         14 |          1        0.04       99.96
         18 |          1        0.04      100.00
------------+-----------------------------------
      Total |      2,442      100.00

My questions are:

1. Could these variables (which appear to be discrete variables to me, is that so?; or are they categorical variables instead?) be treated as continuous in the model.

2. What would be better: mean (SD) or median (IQR) for these variables?

3. If I wanted to compare means with a variable expressed in tertiles, could I use Kruskal-Wallis test?

Thank you in advance.