If he cam sit with support and actually do all the other things you say , then motor milestones are normal . Head may still wobble a bit during sudden movements . That is normal . So keep a watch and consult your pediatrician for complete developmental assessment . Watch for other milestones like smiling , vocalisation , cooing , his hand movements etc .
Next Steps
Detailed consultation with your paediatrician
Health Tips
Never try to pull up a child by thumb or hand . it can dislocate the elbow . Always put hands under the armpits to lift up a child .