That mortar needs serious repointing. It might require taking down the upper courses and rebuilding. As Neal says (Neal is ALWAYS RIGHT) get an expert to do the evaluation. Money well spent. However, fireplace repointing is NOT a beginner job. Building a low block wall is a beginner job to learn proper joint grouting, leveling, alignment ... I really like your enthusiasm. Remember to celebrate each point in your series of successes. Remodeling can seem to drag forever, so break up the long slog by enjoying a segment of the job "well done." This will help your relationship and make the project a lot more fun.