At a first glance, your spectrum is a little strange...
Since you are representing transmittance in YY axis, I presume that you prepared the sample in KBr pellets and used FTIR in transmittance mode.
I´m saying that the spectrum is strange because it doesn´t have a normal baseline. The "peaks" at around 1250 and 1800 cm-1 make no sense because they pass beyond the baseline. This makes me think that the spectrum that you showed me was not obtained directly, but results from a mathematic operation. Did you try to subtract the spectrum of any component (reagent)?
If you represent this spectrum in Absorbance (if you used the ATR mode, that´s the most correct way), you will see that the mentioned "peaks" come as negative peaks and you may readly understand that something is wrong here.
When you mention weak peaks at 1500-1700 cm-1 or at 3000-3500 cm-1, I don´t understand your question very well. These are, in fact, the most intense peaks of the spectrum.
Attached File- To help you understand very quickly, I made some picture changes to the spectrum that you showed me. It´s just a rough simulation… In A, it shows the appearance of your spectrum when the YY axis is absorbance, and I putted the baseline in place. In B, I erased the peaks that should not be there. This is just a drawing, please don´t forget it!... it doesn´t mean that a new spectrum will look exactly like that.
So, after this starting point, I recommend you to repeat the FTIR analysis, using a well dried sample. No matter the method (ATR or transmittance) that you will use, try to represent the spectrum in Absorbance versus wavenumber. That kind of graphic is easier to understand relatively to the baseline. You can not have negative peaks!
Even better, start by obtaining a spectrum of a simple molecule from which you have a reliable spectrum in the literature. Only after that, repeat the FTIR of your sample because this result that you showed me seems to reflect some mistakes. Run the spectrum between 400 or 500 cm-1 and 4000 cm-1. Below 500 cm-1, the equipment is not very accurate.
As for the attribution of the peaks, it´s probable that the peak around 1600 cm-1 is originated from the carbonyl group of EDTA and the large band at 3000-3500 cm-1 is typical of OH elongation mode (this hydroxyde can come from the reagents or from the water or other solvents with this group). But wait for the new spectrum, the result may be different from this one. Ah, and the low intensity peaks around 2300 cm-1 are contaminations from the atmosphere, these peaks are not from the sample.
The information from EDX gives you only the approximate percentage of chemical elements. EDX works by detecting the x-rays from electronic transitions within the atom. This doesn´t match FTIR that detects the dipolar moment variations in chemical bonds, resulting from certain types of vibrations (not all vibrations are active in the infrared due to this process; sometimes we use Raman spectroscopy – it detects polarisability variations- to detect other vibrations in the infrared region).
In your experiment, EDX is only useful to confirm the presence and relative amounts of the chemical elements of your system: Te, Pb, C, O, N, etc…It does not confirm which molecules are there, or if your reaction went well!