How to make rendang beef with a smooth and consistent texture?
A cheap food processor is usually just fine for this type of application, I used a stick blender for years to make curry pastes with good results. Although, if it's a really cheap and nasty one it may not do much for you. 

The trick is to chop hard ingredients before blending. Galangal is very hard and will take forever to blend unless you cut it into pieces first. For lemongrass I suggest cutting it lengthways and then cutting into 1 inch or so pieces - bash the fat end with the back of a knife and throw away the pithy hard plug that comes out first.  

As for sourness tamarind is not a universal product, you get different intensities throughout the world so you may need to add less. However, it sounds like you overdid the lime a bit, lime leaves aren't that sour so zest and juice from a lime is a bit much. However, you can add more sugar (palm sugar is great) to balance it out. It all depends on how sweet and sour you want it.