Generally, you need a DICOM viewer to open your X-ray images (you can google for a free one). But, determining the parameters mainly depends on the X-ray imaging device and the acquired images (radiography / fluoroscopy vs CT vs ...):
- Dose is typically included in the DICOM header during image acquisition
In addition, dose is measured during your regular quality assuarance procedure using dosimetry equipment. Concluding dose from the acquired images (grey values) is not very common and needs special calibration.
- Parameters such as resolution / MTF, noise, contrast, ... are typically checked during your regular quality assurance procedures using special phantoms (including lead patterns, high and low contrast objects, slanted-edge objects, different materials for HU stability of CT,...) and predefined image acquisition protocols. The parameters are mostly determined by visual evaluation of the images. Alternatively, some automatic software tools are used mostly delivered by the manufacturer of the X-ray device. But this software needs to be adapted to the phantom / acquired images. For example, determining the MTF of CR images can be done in different ways using a special lead pattern, a thin-wire object or a slanted-edge object (maybe there are more methods).
So, I think you can use a simple DICOM viewer and determine the parameters by visual evaluation (needs respective phantoms). If you want to automize this and be more objective in parameter determination, you need to program your own software based on DICOM viewing ability. We used ImageJ (DICOM viewer, macro-based programming) and Python programming language (add-on packages: Pydicom, PyQt, Scikit-image) to solve such tasks.
No, you get the MTF by putting an absorbing edge slightly tilted with respect to the pixels of your detector. The plugin takes your measured data and gives you MTF and SNR. There is quite a comprehensive manual online.
The details for experimental measurements of image quality parameters and patient dose for a CT scanner image are described in my review article: Quality assurance of computed tomography scanners, available in my portion of RG website here. For conventional radiographic equipments, the methods for image quality analysis are similar. Dose measurements using a pencil ionisation chamber for a CT scanner are fully discussed in my review article. For projection x-Ray, CR and DR imaging systems, the patient dose can be measured with many types low energy ionisation chamber- electrometer systems available commercially from a host of manufacturers. Alternatively, TL and OSL dosimeters can also be used to measure entrance skin dose(ESD) of a patient. The manufacturer of CT scanners provide the software for evaluate the MTF of an image using their test gadgets. Several multipurpose phantoms for measuring the image quality parameters are also available commercially. See the technical literature from the catalogues of manufacturers. If you require the basics of these measurements, there are several medical imaging text books available, e.g., Christensen's physics of diagnostic radiology or other references cited in my review paper above. Hope the above is helpful.