Automatic Grammar Error Correction (GEC) is a classic NLP challenge that has been applied to language education, professional writing aid, and cross-lingual communication. Despite considerable progress with pre-trained Transformer architectures, high-performance GEC systems have three common weaknesses: lack of explicit syntactic dependency modelling, non-differentiated treatment of qualitatively different types of errors and imperfect ability to absorb post-deployment user feedback. In order to close these gaps, the present paper presents an end-to-end model, called HiGATGEC (Hierarchical Graph-Attention Transformer for Grammar Error Correction), that is built on a BERT encoder, a relation-conditioned two-layer Graph Attention Network (GAT) over Universal Dependency (UD) parse trees, an autoregressive decoder with a Grammar-Confidence Gate (GCG), and an online continual learning loop using Low-Rank Adaptation (LoRA). Errors are corrected at four linguistic levels: lexical, syntactic, semantic, and pragmatic. Experiments are performed on CoNLL-2014, BEA-2019 and JFLEG across five independent runs (mean ± SD), the contribution of each component is ablated, and statistical significance is assessed using a two-tailed paired t-test (α = 0.05). HiGATGEC achieves F0.5 = 67.83 ± 0.31 on CoNLL-2014 (p = 0.008 vs. GECToR-XL), F0.5 = 71.24 ± 0.28 on BEA-2019, and BLEU = 72.41 ± 0.44 on JFLEG, representing the highest scores among all evaluated baselines. Three simulated deployment cycles of online feedback further improved performance. These findings indicate that explicit syntactic graph modelling, hierarchical error weighting and dynamic feedback adaptation can yield reliable and repeatable improvements in GEC, offering a promising foundation for AI-aided writing systems in educational and professional settings.