Just doing this with formulas is rather limiting.
The following will give you some of the features you want, and it works in OpenOffice.
I left row 1 & 2 empty to leave room for some more headings if required.
Rows 3 & 4 are headings
Each Tenant takes up two rows, so that date of payment is on one row and amount paid is on the next row.
To make this work each payment is recorded along with the payment date. I have used columns P to HO for the payment record. For someone paying weekly this would last for 4 years.
Enter the following text in cells. If I have two cells for one text, merge the cells and centre the text, and enter the text once.
B3 Name C3 Address D3 Weekly
E3/F3 First Payment
G3/H3 Start of tenancy
I3/J3 Last payment
M3/N3 Paid until
D4 Rate E4 $ F4 Date G4 Date H4 Day I4 $
J4 Date K4 $ L4 Days M4 Week of N4 Day O4 record
Other rows O5 date O6 $
Enter these formulas:
Select cells D5 to O6
Now drag these cells down, as many pairs of rows as you have tenants.
The formulas all test the weekly rate and if the weekly rate is empty, the formulas all return ""
For the first tenant, add data in cells D5 to G5 and enter dates and payment amounts (after the initial payment) starting with first regular payment date in P5 and amount in P6.
I hope that this gives you something to work on.
I haven't tested this with much data so you need to look at results closely when you first start using it, to be sure it is doing what you expect.
One problem is that when you change weekly rates you will need to start a new pair of rows as the paid until calculation is based on one weekly rate.